A reduction principle for Fourier coefficients of automorphic forms [PDF]
Mathematische Zeitschrift, 2020 In this paper we analyze a general class of Fourier coefficients of automorphic forms on reductive adelic groups $\mathbf{G}(\mathbb{A}_\mathbb{K})$ and their covers.
Gourevitch, Dmitry +4 more
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Eulerianity of Fourier coefficients of automorphic forms [PDF]
Representation Theory of the American Mathematical Society, 2021 We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a ‘hidden’ invariance property of Fourier coefficients.
Gourevitch, D. +4 more
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Growth of Fourier coefficients of vector-valued automorphic forms
Journal of Number Theory, 2023 In this article, we establish polynomial-growth bound for the sequence of Fourier coefficients associated to even integer weight vector-valued automorphic forms of Fuchsian groups of the first kind. At the end, their $L$-functions and exponential sums have been discussed.
Bajpai, Jitendra +2 more
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Fourier coefficients of GL(N) automorphic forms in arithmetic progressions [PDF]
Geometric and Functional Analysis, 2014 We show that the multiple divisor functions of integers in invertible residue classes modulo a prime number, as well as the Fourier coefficients of GL(N) Maass cusp forms for all N larger than 2, satisfy a central limit theorem in a suitable range, generalizing the case N=2 treated by E. Fouvry, S. Ganguly, E. Kowalski and P. Michel.
Kowalski, Emmanuel, Ricotta, Guillaume
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Arthur Parameters and Fourier coefficients for Automorphic Forms on Symplectic Groups [PDF]
, 2015 We study the structures of Fourier coefficients of automorphic forms on symplectic groups based on their local and global structures related to Arthur parameters.
Jiang, Dihua, Liu, Baiying
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On an analogue of the Ichino--Ikeda conjecture for Whittaker coefficients on the metaplectic group [PDF]
, 2016 In previous papers we formulated an analogue of the Ichino--Ikeda conjectures for Whittaker--Fourier coefficients of automorphic forms on classical group and the metaplectic group. In the latter case we reduced the conjecture to a local identity. In this
Lapid, Erez, Mao, Zhengyu
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Automorphic Instanton Partition Functions on Calabi-Yau Threefolds [PDF]
, 2011 We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main focus lies on the
Alexandrov S +60 more
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Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors [PDF]
, 2014 Motivated by string theory scattering amplitudes that are invariant under a discrete U-duality, we study Fourier coefficients of Eisenstein series on Kac-Moody groups. In particular, we analyse the Eisenstein series on $E_9(R)$, $E_{10}(R)$ and $E_{11}(R)
Fleig, Philipp +2 more
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On Atkin and Swinnerton-Dyer Congruence Relations (2)
, 2007 In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at ...
Atkin, A. O. L. +2 more
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The Arithmetic of the Fourier Coefficients of Automorphic Forms
, 2023 PhD thesis, 141 pages.
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