Results 11 to 20 of about 8,516 (148)
Fourier expansion of light‐cone Eisenstein series
Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2175-2247, December 2023., 2023 Abstract In this work, we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n+1$n+1$‐space. As a consequence, we obtain results on location of all poles of these Eisenstein series as well as their supremum norms.
Dubi Kelmer, Shucheng Yu
wiley +1 more source
Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations
Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2436-2490, December 2023., 2023 Abstract Let X$X$ be a smooth, separated, geometrically connected scheme defined over a number field K$K$ and {ρλ:π1(X)→GLn(Eλ)}λ$\lbrace \rho _\lambda :\pi _1(X)\rightarrow \mathrm{GL}_n(E_\lambda )\rbrace _\lambda$ a system of semisimple λ$\lambda$‐adic representations of the étale fundamental group of X$X$ such that for each closed point x$x$ of X$X$
Chun Yin Hui
wiley +1 more source
Perfectoid Shimura varieties and the Calegari–Emerton conjectures
Journal of the London Mathematical Society, Volume 108, Issue 5, Page 1954-2000, November 2023., 2023 Abstract We prove many new cases of a conjecture of Calegari–Emerton describing the qualitative properties of completed cohomology. The heart of our argument is a careful inductive analysis of completed cohomology on the Borel–Serre boundary. As a key input to this induction, we prove a new perfectoidness result for towers of minimally compactified ...
David Hansen, Christian Johansson
wiley +1 more source
Monodromy of four‐dimensional irreducible compatible systems of Q$\mathbb {Q}$
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1773-1790, August 2023., 2023 Abstract Let F$F$ be a totally real field and n⩽4$n\leqslant 4$ a natural number. We study the monodromy groups of any n$n$‐dimensional strictly compatible system {ρλ}λ$\lbrace \rho _\lambda \rbrace _\lambda$ of λ$\lambda$‐adic representations of F$F$ with distinct Hodge–Tate numbers such that ρλ0$\rho _{\lambda _0}$ is irreducible for some λ0$\lambda ...
Chun Yin Hui
wiley +1 more source
The Group of Automorphisms of the Modular Function Field
Inventiones Mathematicae, 1971 Let F be the field of modular functions of all levels on the upper half plane, with, say, Fourier coefficients in the field of all roots of unity. One can define in an obvious way two types of automorphisms of F. First we note that F is a Galois extension of Q(j), where j is the modular function. We have therefore the Galois group U of automorphisms of
openaire +1 more source
, 2010 We define two-parameter generalizations of Andrews' $(k+1)$-marked odd Durfee symbols and $2k$th symmetrized odd rank moments, and study the automorphic properties of some of their generating functions.
Andrews +8 more
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The Highly Oscillatory Behavior of Automorphic Distributions for SL(2)
, 2004 Automorphic distributions for SL(2) arise as boundary values of modular forms and, in a more subtle manner, from Maass forms. In the case of modular forms of weight one or of Maass forms, the automorphic distributions have continuous first ...
A. Zygmund +10 more
core +1 more source
Eichler cohomology in general weights using spectral theory [PDF]
, 2016 In this paper, we construct a pairing between modular forms of positive real weight and elements of certain Eichler cohomology groups that were introduced by Knopp in 1974.
Neururer, Michael
core +2 more sources
Generalized moonshine II: Borcherds products
, 2012 The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and ...
Carnahan, Scott
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Modular Solutions to Equations of Generalized Halphen Type
, 1998 Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions all uniformize Riemann surfaces of genus zero and have
Dedekind R. +7 more
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