Publications

2013

• Sharp Estimates for Turbulence in White-Forced Generalised Burgers Equation
  
  • Boritchev Alexandre
  Geometric And Functional Analysis, Springer Verlag, 2013, 23, pp.1730 - 1771. We consider the non-homogeneous generalised Burgers equation$$∂u/∂t + f (u) ∂u/∂x − \nu ∂^2u/∂x^2 = η, t ≥ 0, x ∈ S^1 .$$Here $f$ is strongly convex and satisfies a growth condition, $\nu$ is small and positive, while $\eta$ is a random forcing term, smooth in space and white in time. For any solution $u$ of this equation we consider the quasi-stationary regime, corresponding to $t ≥ T_1$ , where $T_1$ depends only on $f$ and on the distribution of $η$. We obtain sharp upper and lower bounds for Sobolev norms of u averaged in time and in ensemble. These results yield sharp upper and lower bounds for natural analogues of quantities characterising the hydrodynamical turbulence. All our bounds do not depend on the initial condition or on $t$ for$ t ≥ T_1$ , and hold uniformly in $\nu$. Estimates similar to some of our results have been obtained by Aurell, Frisch, Lutsko and Vergassola on a physical level of rigour; we use an argument from their article. (10.1007/s00039-013-0245-4)
  DOI : 10.1007/s00039-013-0245-4
• On the selection of the classical limit for potentials with BV derivatives
  
  • Athanassoulis Agissilaos
  • Paul Thierry
  Journal of Dynamics and Differential Equations, Springer Verlag, 2013, 25 (1), pp.33-47. We consider the classical limit of the quantum evolution, with some rough potential, of wave packets concentrated near singular trajectories of the underlying dynamics. We prove that under appropriate conditions, even in the case of BV vector fields, the correct classical limit can be selected.
• Normal surface singularities admitting contracting automorphisms
  
  • Favre Charles
  • Ruggiero Matteo
  Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc, 2013. We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting automorphism. (10.5802/afst.1425)
  DOI : 10.5802/afst.1425
• Wild Hodge theory and Hitchin-Kobayashi correspondence [after T. Mochizuki]
  
  • Sabbah Claude
  Asterisque, Société Mathématique de France, 2013, 352, pp.Exposé n°2050. T. Mochizuki constructs a theory of variations of wild Hodge structure for which the underlying flat connection can have irregular singularities at infinity. He extends in this way the correspondence of Corlette and Simpson between irreducible flat bundles and stables Higgs bundles, taking into account objects with irregular singularities. As an application, he proves a conjecture of Kashiwara concerning a generalization of the Hard Lefschetz theorem when the coefficients are the de Rham complex of a simple holonomic D-module on smooth complex projective variety.
• On the convergence to equilibrium for degenerate transport problems
  
  • Bernard Etienne
  • Salvarani Francesco
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2013, 208 (3), pp.977-984. We give a counterexample which shows that the asymptotic rate of convergence to the equilibrium state for the transport equation, with a degenerate cross section and in the periodic setting, cannot be better than $t^{-1/2}$ in the general case. We suggest moreover that the geometrical properties of the cross section are the key feature of the problem and impose, through the distribution of the forward exit time, the speed of convergence to the stationary state. (10.1007/s00205-012-0608-2)
  DOI : 10.1007/s00205-012-0608-2
• LOFAR detections of low-frequency radio recombination lines towards Cassiopeia A
  
  • Asgekar Ashish
  • Oonk J. B. R.
  • Yatawatta S.
  • van Weeren R. J.
  • Mckean J. P.
  • White G.
  • Jackson N.
  • Anderson J.
  • Avruch I. M.
  • Batejat F.
  • Beck R.
  • Bell M. E.
  • Bell M. R.
  • van Bemmel I.
  • Bentum M. J.
  • Bernardi G.
  • Best P.
  • Birzan L.
  • Bonafede A.
  • Braun R.
  • Breitling F.
  • van de Brink R. H.
  • Broderick J.
  • Brouw W. N.
  • Bruggen M.
  • Butcher H. R.
  • van Cappellen W.
  • Ciardi B.
  • Conway J. E.
  • de Gasperin F.
  • de Geus E.
  • de Jong A.
  • de Vos M.
  • Duscha S.
  • Eisloffel J.
  • Falcke H.
  • Fallows R. A.
  • Ferrari C.
  • Frieswijk W.
  • Garrett M. A.
  • Griessmeier Jean-Mathias
  • Grit T.
  • Gunst A. W.
  • Hassall T. E.
  • Heald G.
  • Hessels J. W. T.
  • Hoeft M.
  • Iacobelli M.
  • Intema H.
  • Juette E.
  • Karastergiou A.
  • Kohler J.
  • Kondratiev V. I.
  • Kuniyoshi M.
  • Kuper G.
  • Law C.
  • van Leeuwen J.
  • Maat P.
  • Macario G.
  • Mann G.
  • Markoff S.
  • Mckay-Bukowski D.
  • Mevius M.
  • Miller-Jones J. C. A.
  • Mol J. D.
  • Morganti R.
  • Mulcahy D. D.
  • Munk H.
  • Norden M. J.
  • Orru E.
  • Paas H.
  • Pandey-Pommier M.
  • Pandey V. N.
  • Pizzo R.
  • Polatidis A. G.
  • Reich W.
  • Rottgering H.
  • Scheers B.
  • Schoenmakers A.
  • Sluman J.
  • Smirnov O.
  • Sobey C.
  • Steinmetz M.
  • Tagger Michel
  • Tang Y.
  • Tasse C.
  • Vermeulen R.
  • Vocks C.
  • Wijers R. A. M. J.
  • Wise M. W.
  • Wucknitz O.
  • Zarka P.
  Astronomy & Astrophysics - A&A, EDP Sciences, 2013, 551 (L11), pp.5 pages. Cassiopeia A was observed using the Low-Band Antennas of the LOw Frequency ARray (LOFAR) with high spectral resolution. This allowed a search for radio recombination lines (RRLs) along the line-of-sight to this source. Five carbon-alpha RRLs were detected in absorption between 40 and 50 MHz with a signal-to-noise ratio of > 5 from two independent LOFAR datasets. The derived line velocities (v_LSR ~ -50 km/s) and integrated optical depths (~ 13 s^-1) of the RRLs in our spectra, extracted over the whole supernova remnant, are consistent within each LOFAR dataset and with those previously reported. For the first time, we are able to extract spectra against the brightest hotspot of the remnant at frequencies below 330 MHz. These spectra show significantly higher (15-80 %) integrated optical depths, indicating that there is small-scale angular structure on the order of ~1 pc in the absorbing gas distribution over the face of the remnant. We also place an upper limit of 3 x 10^-4 on the peak optical depths of hydrogen and helium RRLs. These results demonstrate that LOFAR has the desired spectral stability and sensitivity to study faint recombination lines in the decameter band. (10.1051/0004-6361/201221001)
  DOI : 10.1051/0004-6361/201221001
• Intrication quantique/classique
  
  • Paul Thierry
  InFluxus, InFluxus, 2013. Nous discutons certains liens reliant les paradigmes classique et quantique non pas en tentant d'établir comment l'un se résout á l'autre, mais plutôt en montrant un certain enchevêtrement, une intrication entre ces deux mondes. Aprés avoir discuté de l'incidence du classique sur le quantique, par exemple dans la construction des objets dynamiques, nous montrons comment des traces quantiques peuvent perdurer á la limite classique. Nous établissons enfin comment les deux notions si ''typées" d'imprédictibilité (classique) et d'indéterminisme (quantique) se superpose dans certaines situations.
• Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones.
  
  • Pacard Frank
  • Wei Juncheng
  Journal of Functional Analysis, Elsevier, 2013, 264 (5), pp.1131-1167. For all n \geq 1, we are interested in bounded solutions of the Allen-Cahn equation \Delta u+ u− u^3 = 0 which are defined in all R^{n+1} and whose zero set is asymptotic to a given minimal cone. In particular, in dimension n + 1 \geq 8, we prove the existence of stable solutions of the Allen-Cahn equation whose zero sets are not hyperplanes. (10.1016/j.jfa.2012.03.010)
  DOI : 10.1016/j.jfa.2012.03.010
• Local exact controllability of a 1D Bose-Einstein condensate in a time-varying box
  
  • Beauchard Karine
  • Lange Horst
  • Holger Teismann
  , 2013. We consider a one dimensional Bose-Einstein condensate in a in finite square-well (box) potential. This is a nonlinear control system in which the state is the wave function of the Bose Einstein condensate and the control is the length of the box. We prove that local exact controllability around the ground state (associated with a fi xed length of the box) holds generically with respect to the chemical potential ; i.e. up to an at most countable set of values. The proof relies on the linearization principle and the inverse mapping theorem, as well as ideas from analytic perturbation theory.
• Restricted inverse zero-sum problems in groups of rank two
  
  • Schmid Wolfgang A.
  Quarterly Journal of Mathematics, Oxford University Press (OUP), 2013, 63 (2), pp.477-487. Let $(G,+)$ be a finite abelian group. Then, $\so(G)$ and $\eta(G)$ denote the smallest integer $\ell$ such that each sequence over $G$ of length at least $\ell$ has a subsequence whose terms sum to $0$ and whose length is equal to and at most, resp., the exponent of the group. For groups of rank two, we study the inverse problems associated to these constants, i.e., we investigate the structure of sequences of length $\so(G)-1$ and $\eta(G)-1$ that do not have such a subsequence. On the one hand, we show that the structure of these sequences is in general richer than expected. On the other hand, assuming a well-supported conjecture on this problem for groups of the form $C_m \oplus C_m$, we give a complete characterization of all these sequences for general finite abelian groups of rank two. In combination with partial results towards this conjecture, we get unconditional characterizations in special cases. (10.1093/qmath/haq042)
  DOI : 10.1093/qmath/haq042
• Introduction.
  
  • Kosmann-Schwarzbach Yvette
  , 2013, pp.1-17.
• On the Characterization of Pseudodifferential Operators (Old and New)
  
  • Bony Jean-Michel
  , 2013, pp.21-34. In the framework of the Weyl-Hörmander calculus, under a condition of "geodesic temperance", pseudodifferential operators can be characterized by the boundedness of their iterated commutators. As a corollary, functions of pseudodifferential operators are themselves pseudodifferential. Sufficient conditions are given for the geodesic temperance. In particular, it is valid in the Beals-Fefferman calculus. (10.1007/978-1-4614-6348-1_2)
  DOI : 10.1007/978-1-4614-6348-1_2
• Top Coefficients of the Denumerant
  
  • Baldoni Velleda
  • Berline Nicole
  • Dutra Brandon
  • Köppe Matthias
  • Vergne Michele
  • de Loera Jesus
  Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), pp.1149-1160. For a given sequence $\alpha = [\alpha_1,\alpha_2,\ldots , \alpha_N, \alpha_{N+1}]$ of $N+1$ positive integers, we consider the combinatorial function $E(\alpha)(t)$ that counts the nonnegative integer solutions of the equation $\alpha_1x_1+\alpha_2 x_2+ \ldots+ \alpha_Nx_N+ \alpha_{N+1}x_{N+1}=t$, where the right-hand side $t$ is a varying nonnegative integer. It is well-known that $E(\alpha)(t)$ is a quasipolynomial function of $t$ of degree $N$. In combinatorial number theory this function is known as the $\textit{denumerant}$. Our main result is a new algorithm that, for every fixed number $k$, computes in polynomial time the highest $k+1$ coefficients of the quasi-polynomial $E(\alpha)(t)$ as step polynomials of $t$. Our algorithm is a consequence of a nice poset structure on the poles of the associated rational generating function for $E(\alpha)(t)$ and the geometric reinterpretation of some rational generating functions in terms of lattice points in polyhedral cones. Experiments using a $\texttt{MAPLE}$ implementation will be posted separately. (10.46298/dmtcs.2373)
  DOI : 10.46298/dmtcs.2373
• On the monodromy of the Hitchin connection
  
  • Laszlo Yves
  • Pauly Christian
  • Sorger Christoph
  Journal of Geometry and Physics, Elsevier, 2013, 64, pp.64-78. We show that the image of the monodromy representation of the Hitchin connection on the sheaf of generalized SL(2)-theta functions over a family of complex smooth projective curves of genus g > 2 contains an element of infinite order. (10.1016/j.geomphys.2012.11.003)
  DOI : 10.1016/j.geomphys.2012.11.003
• LOFAR: The LOw-Frequency ARray
  
  • van Haarlem M. P.
  • Wise M. W.
  • Gunst A. W.
  • Heald G.
  • Mckean J. P.
  • Hessels J. W. T.
  • de Bruyn A. G.
  • Nijboer R.
  • Swinbank J.
  • Fallows R.
  • Brentjens M.
  • Nelles A.
  • Beck R.
  • Falcke H.
  • Fender R.
  • Hörandel J.
  • Koopmans L. V. E.
  • Mann G.
  • Miley G.
  • Röttgering H.
  • Stappers B. W.
  • Wijers R. A. M. J.
  • Zaroubi S.
  • Akker M. van Den
  • Alexov A.
  • Anderson J.
  • Anderson K.
  • van Ardenne A.
  • Arts M.
  • Asgekar A.
  • Avruch I. M.
  • Batejat F.
  • Bähren L.
  • Bell M. E.
  • Bell M. R.
  • van Bemmel I.
  • Bennema P.
  • Bentum M. J.
  • Bernardi G.
  • Best P.
  • Bîrzan L.
  • Bonafede A.
  • Boonstra A. -J.
  • Braun R.
  • Bregman J.
  • Breitling F.
  • van de Brink R. H.
  • Broderick J.
  • Broekema P. C.
  • Brouw W. N.
  • Brüggen M.
  • Butcher H. R.
  • van Cappellen W.
  • Ciardi B.
  • Coenen T.
  • Conway J.
  • Coolen A.
  • Corstanje A.
  • Damstra S.
  • Davies O.
  • Deller A. T.
  • Dettmar R. -J.
  • van Diepen G.
  • Dijkstra K.
  • Donker P.
  • Doorduin A.
  • Dromer J.
  • Drost M.
  • van Duin A.
  • Eislöffel J.
  • van Enst J.
  • Ferrari C.
  • Frieswijk W.
  • Gankema H.
  • Garrett M. A.
  • de Gasperin F.
  • Gerbers M.
  • de Geus E.
  • Griessmeier Jean-Mathias
  • Grit T.
  • Gruppen P.
  • Hamaker J. P.
  • Hassall T.
  • Hoeft M.
  • Holties H.
  • Horneffer A.
  • van Der Horst A.
  • van Houwelingen A.
  • Huijgen A.
  • Iacobelli M.
  • Intema H.
  • Jackson N.
  • Jelic V.
  • de Jong A.
  • Juette E.
  • Kant D.
  • Karastergiou A.
  • Koers A.
  • Kollen H.
  • Kondratiev V. I.
  • Kooistra E.
  • Koopman Y.
  • Koster A.
  • Kuniyoshi M.
  • Kramer M.
  • Kuper G.
  • Lambropoulos P.
  • Law C.
  • van Leeuwen J.
  • Lemaitre J.
  • Loose M.
  • Maat P.
  • Macario G.
  • Markoff S.
  • Masters J.
  • Mckay-Bukowski D.
  • Meijering H.
  • Meulman H.
  • Mevius M.
  • Middelberg E.
  • Millenaar R.
  • Miller-Jones J. C. A.
  • Mohan R. N.
  • Mol J. D.
  • Morawietz J.
  • Morganti R.
  • Mulcahy D. D.
  • Mulder E.
  • Munk H.
  • Nieuwenhuis L.
  • van Nieuwpoort R.
  • Noordam J. E.
  • Norden M.
  • Noutsos A.
  • Offringa A. R.
  • Olofsson H.
  • Omar A.
  • Orrú E.
  • Overeem R.
  • Paas H.
  • Pandey-Pommier M.
  • Pandey V. N.
  • Pizzo R.
  • Polatidis A.
  • Rafferty D.
  • Rawlings S.
  • Reich W.
  • de Reijer J. -P.
  • Reitsma J.
  • Renting A.
  • Riemers P.
  • Rol E.
  • Romein J. W.
  • Roosjen J.
  • Ruiter M.
  • Scaife A.
  • van Der Schaaf K.
  • Scheers B.
  • Schellart P.
  • Schoenmakers A.
  • Schoonderbeek G.
  • Serylak M.
  • Shulevski A.
  • Sluman J.
  • Smirnov O.
  • Sobey C.
  • Spreeuw H.
  • Steinmetz M.
  • Sterks C. G. M.
  • Stiepel H. -J.
  • Stuurwold K.
  • Tagger Michel
  • Tang Y.
  • Tasse C.
  • Thomas I.
  • Thoudam S.
  • Toribio M. C.
  • van Der Tol B.
  • Usov O.
  • van Veelen M.
  • van Der Veen A. -J.
  • ter Veen S.
  • Verbiest J. P. W.
  • Vermeulen R.
  • Vermaas N.
  • Vocks C.
  • Vogt C.
  • de Vos M.
  • van Der Wal E.
  • van Weeren R.
  • Weggemans H.
  • Weltevrede P.
  • White S.
  • Wijnholds S. J.
  • Wilhelmsson T.
  • Wucknitz O.
  • Yatawatta S.
  • Zarka P.
  • Zensus A.
  • van Zwieten J.
  Astronomy & Astrophysics - A&A, EDP Sciences, 2013, A2, pp.53 pages. LOFAR, the LOw-Frequency ARray, is a new-generation radio interferometer constructed in the north of the Netherlands and across europe. Utilizing a novel phased-array design, LOFAR covers the largely unexplored low-frequency range from 10-240 MHz and provides a number of unique observing capabilities. Spreading out from a core located near the village of Exloo in the northeast of the Netherlands, a total of 40 LOFAR stations are nearing completion. A further five stations have been deployed throughout Germany, and one station has been built in each of France, Sweden, and the UK. Digital beam-forming techniques make the LOFAR system agile and allow for rapid repointing of the telescope as well as the potential for multiple simultaneous observations. With its dense core array and long interferometric baselines, LOFAR achieves unparalleled sensitivity and angular resolution in the low-frequency radio regime. The LOFAR facilities are jointly operated by the International LOFAR Telescope (ILT) foundation, as an observatory open to the global astronomical community. LOFAR is one of the first radio observatories to feature automated processing pipelines to deliver fully calibrated science products to its user community. LOFAR's new capabilities, techniques and modus operandi make it an important pathfinder for the Square Kilometre Array (SKA). We give an overview of the LOFAR instrument, its major hardware and software components, and the core science objectives that have driven its design. In addition, we present a selection of new results from the commissioning phase of this new radio observatory. (10.1051/0004-6361/201220873)
  DOI : 10.1051/0004-6361/201220873
• Siméon-Denis Poisson. Les mathématiques au service de la science.
  
  • Kosmann-Schwarzbach Yvette
  , 2013, pp.550.
• Moduli space theory for the Allen-Cahn equation in the plane.
  
  • Pacard Frank
  • del Pino Manuel
  • Kowalczyk Michal
  Transactions of the American Mathematical Society, American Mathematical Society, 2013, 365 (2), pp.721-766. In this paper we study entire solutions of the Allen-Cahn equation \Delta u - F'(u) = 0, where F is an even, bistable function. We are particularly interested in the description of the moduli space of solutions which have some special structure at infinity. The solutions we are interested in have their zero set asymptotic to 2k, k >= 2 oriented affine half-lines at infinity and, along each of these affine half-lines, the solutions are asymptotic to the one-dimensional heteroclinic solution: such solutions are called multiple-end solutions, and their set is denoted by M_2k. The main result of our paper states that if u in M_2k is nondegenerate, then locally near u the set of solutions is a smooth manifold of dimension 2k . This paper is part of a program whose aim is to classify all 2k-ended solutions of the Allen-Cahn equation in dimension 2 , for k>=2.
• Introduction to Stokes structures
  
  • Sabbah Claude
  , 2013, pp.viii+249. The purpose of these lectures is to introduce the notion of a Stokes-perverse sheaf as a receptacle for the Riemann-Hilbert correspondence for holonomic D-modules. They develop the original idea of P. Deligne in dimension one, and make it enter the frame of perverse sheaves. They also give a first step for a general definition in higher dimension, and make explicit particular cases of the Riemann-Hilbert correspondence, relying on recent results of T. Mochizuki. (10.1007/978-3-642-31695-1)
  DOI : 10.1007/978-3-642-31695-1
• Some remarks on barycentric-sum problems over cyclic groups
  
  • Ordaz Oscar
  • Plagne Alain
  • Schmid Wolfgang A.
  European Journal of Combinatorics, Elsevier, 2013, 34 (8), pp.1415-1428. We derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer l such that each subset A of G with at least l elements contains a subset with k elements {g_1, ... , g_k} satisfying g_1 + ... + g_k = k g_j for some 1 <= j <= k. (10.1016/j.ejc.2013.05.025)
  DOI : 10.1016/j.ejc.2013.05.025
• Construction of a multi-soliton blow-up solution to the semilinear wave equation in one space dimension
  
  • Côte Raphaël
  • Zaag Hatem
  Communications on Pure and Applied Mathematics, Wiley, 2013, 66 (10), pp.1541-1581. We consider the semilinear wave equation with power nonlinearity in one space dimension. Given a blow-up solution with a characteristic point, we refine the blow-up behavior first derived by Merle and Zaag. We also refine the geometry of the blow-up set near a characteristic point, and show that except may be for one exceptional situation, it is never symmetric with the respect to the characteristic point. Then, we show that all blow-up modalities predicted by those authors do occur. More precisely, given any integer $k\ge 2$ and $\zeta_0 \in \m R$, we construct a blow-up solution with a characteristic point $a$, such that the asymptotic behavior of the solution near $(a,T(a))$ shows a decoupled sum of $k$ solitons with alternate signs, whose centers (in the hyperbolic geometry) have $\zeta_0$ as a center of mass, for all times. (10.1002/cpa.21452)
  DOI : 10.1002/cpa.21452
• Poincaré et la déconstruction du négatif
  
  • Paul Thierry
  , 2013. Nous présentons l'attitude d'Henri Poincaré face aux résultats "négatifs" tels qu'il les a analysés en mécanique céleste et en théorie des quanta.
• Optimal Regularizing Effect for Scalar Conservation Laws
  
  • Golse François
  • Perthame Benoît
  Revista Matemática Iberoamericana, European Mathematical Society, 2013, 29 (2013), pp.1477-1504. We investigate the regularity of bounded weak solutions of scalar conservation laws with convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space. (10.4171/rmi/765)
  DOI : 10.4171/rmi/765
• Remarks on the minimizing geodesic problem in inviscid incompressible fluid mechanics
  
  • Brenier Yann
  Calculus of Variations and Partial Differential Equations, Springer Verlag, 2013, 47 (1-2), pp.55-64. We consider L2 minimizing geodesics along the group of volume preserving maps SDiff(D) of a given 3-dimensional domain D. The corresponding curves describe the motion of an ideal incompressible fluid inside D and are (formally) solutions of the Euler equations. It is known that there is a unique possible pressure gradient for these curves whenever their end points are fixed. In addition, this pressure field has a limited but unconditional (internal) regularity. The present paper completes these results by showing: (1) the uniqueness property can be viewed as an infinite dimensional phenomenon (related to the possibility of relaxing the corresponding minimization problem by convex optimization), which is false for finite dimensional configuration spaces such as O(3) for the motion of rigid bodies; (2) the unconditional partial regularity is necessarily limited. (10.1007/s00526-012-0510-7)
  DOI : 10.1007/s00526-012-0510-7
• Hodge theory of the middle convolution
  
  • Dettweiler Michael
  • Sabbah Claude
  Publications of the Research Institute for Mathematical Sciences, European Mathematical Society, 2013, 49 (4), pp.761-800. We compute the behaviour of Hodge data by tensor product with a unitary rank-one local system and middle convolution by a Kummer unitary rank-one local system for an irreducible variation of polarized complex Hodge structure on a punctured complex affine line. We give applications of these formulas to local systems with G_2-monodromy. (10.4171/PRIMS/119)
  DOI : 10.4171/PRIMS/119
• Construction of automorphic Galois representations II
  
  • Chenevier Gaëtan
  • Harris Michael
  Cambridge Math. Journal, 2013, 1, pp.53-73.