Results 1 to 10 of about 170 (146)
Periods and global invariants of automorphic representations
Journal of Number Theory, 2023 We consider periods of automorphic representations of adele groups defined by integrals along Gelfand subgroups. We define natural maps between local components of such periods and construct corresponding global maps using automorphic $L$-functions. This leads to an introduction of a global invariant of an automorphic representation arising from two ...
André Reznikov, Joseph Bernstein
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Central morphisms and cuspidal automorphic representations [PDF]
Journal of Number Theory, 2019 Let $F$ be a global field. Let $G$ and $H$ be two connected reductive group defined over $F$ endowed with an $F$-morphism $f: H\rightarrow G$ such that the induced morphism $H_{der}\rightarrow G_{der}$ on the derived groups is a central isogeny. Our main results yield in particular the following theorem: Given any irreducible cuspidal representation $π$
Joachim Schwermer
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Cohomology of moduli spaces via a result of Chenevier and Lannes [PDF]
Épijournal de Géométrie Algébrique, 2023 We use a classification result of Chenevier and Lannes for algebraic automorphic representations together with a conjectural correspondence with $\ell$-adic absolute Galois representations to determine the Euler characteristics (with values in the ...
Jonas Bergström, Carel Faber
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Seven Small Simple Groups Not Previously Known to Be Galois Over
Mathematics, 2022 In this note we realize seven small simple groups as Galois groups over Q. The technique that we employ is the determination of the images of Galois representations attached to modular and automorphic forms, relying in two cases on recent results of ...
Luis Dieulefait +2 more
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Chow groups and L-derivatives of automorphic motives for unitary groups, II.
Forum of Mathematics, Pi, 2022 In this article, we improve our main results from [LL21] in two directions: First, we allow ramified places in the CM extension $E/F$ at which we consider representations that are spherical with respect to a certain special maximal compact subgroup, by ...
Chao Li, Yifeng Liu
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An Automorphic Distance Metric and Its Application to Node Embedding for Role Mining
Complexity, 2021 Role is a fundamental concept in the analysis of the behavior and function of interacting entities in complex networks. Role discovery is the task of uncovering the hidden roles of nodes within a network.
Víctor Martínez +2 more
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Application of automorphic forms to lattice problems
Journal of Mathematical Cryptology, 2022 In this article, we propose a new approach to the study of lattice problems used in cryptography. We specifically focus on module lattices of a fixed rank over some number field.
Düzlü Samed, Krämer Juliane
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On fields of rationality for automorphic representations [PDF]
Compositio Mathematica, 2014 Abstract This paper proves two results on the field of rationality $\mathbb{Q}({\it\pi})$ for an automorphic representation
Shin, Sug Woo, Templier, Nicolas
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Forum of Mathematics, Sigma, 2014 We prove a simple level-raising result for regular algebraic, conjugate self-dual automorphic forms on $\mathrm{GL}_n$ .
JACK A. THORNE
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Representations of automorphism groups on the homology of matroids [PDF]
European Journal of Combinatorics, 2021 Given a group $G$ of automorphisms of a matroid $M$, we describe the representations of $G$ on the homology of the independence complex of the dual matroid $M^*$. These representations are related with the homology of the lattice of flats of $M$, and (when $M$ is realizable) with the top cohomology of a hyperplane arrangement.
Moci Luca, GIan Marco Pezzoli
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