Toroidal automorphic forms, Waldspurger periods and double Dirichlet series
, 2011 The space of toroidal automorphic forms was introduced by Zagier in the 1970s: a GL_2-automorphic form is toroidal if it has vanishing constant Fourier coefficients along all embedded non-split tori. The interest in this space stems (amongst others) from
Alain Connes +14 more
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p-adic Eisenstein series and L-functions of certain cusp forms on definite unitary groups
, 2014 We construct p-adic families of Klingen Eisenstein series and L-functions for cuspforms (not necessarily ordinary) unramified at an odd prime p on definite unitary groups of signature (r, 0) (for any positive integer r) for a quadratic imaginary field ...
Eischen, Ellen, Wan, Xin
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Fourier coefficients of automorphic forms and integrable discrete series
Journal of Functional Analysis, 2016 Let $G$ be the group of $\mathbb R$--points of a semisimple algebraic group $\mathcal G$ defined over $\mathbb Q$. Assume that $G$ is connected and noncompact. We study Fourier coefficients of Poincar\' e series attached to matrix coefficients of integrable discrete series.
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The Igusa modular forms and ``the simplest'' Lorentzian Kac--Moody algebras
, 1996 We find automorphic corrections for the Lorentzian Kac--Moody algebras with the simplest generalized Cartan matrices of rank 3: A_{1,0} = 2 0 -1 0 2 -2 -1 -2 2 and A_{1,I} = 2 -2 -1 -2 2 -1 -1 -1 2 For A_{1,0} this correction is given
Gritsenko, Valeri A. +1 more
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Fourier coefficients of automorphic forms, character variety orbits, and small representations
Journal of Number Theory, 2012 We consider the Fourier expansions of automorphic forms on general Lie groups, with a particular emphasis on exceptional groups. After describing some principles underlying known results on GL(n), Sp(4), and G_2, we perform an analysis of the expansions on split real forms of E_6 and E_7 where simplifications take place for automorphic realizations of ...
Miller, Stephen D., Sahi, Siddhartha
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A Test for Identifying Fourier Coefficients of Automorphic Forms and Application to Kloosterman Sums [PDF]
Experimental Mathematics, 2000 We present a numerical test for determining whether a given set of numbers is the set of Fourier coefficients of a Maass form, without knowing its eigenvalue. Our method extends directly to consideration of holomorphic newforms. The test is applied to show that the Kloosterman sums ±S(l, 1; p)/√p are not the coefficients of a Maass form with small ...
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Computation of Fourier coefficients of automorphic forms of type $$G_2$$
Research in Number TheoryIn a recent work, we found formulas for the Fourier coefficients of automorphic forms of type $G_2$: holomorphic Siegel modular forms on $\mathrm{Sp}_6$ that are theta lifts from $G_2^c$, and cuspidal quaternionic modular forms on split $G_2$. We have implemented these formulas in the mathematical software SAGE.
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Eisenstein series and automorphic representations
, 2015 We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles A,
Fleig, Philipp +3 more
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Euler products and Fourier coefficients of automorphic forms on symplectic groups
Inventiones Mathematicae, 1994 The standard \(L\)-function attached to a Siegel modular form of degree \(n\) (or more generally an automorphic form on the adelic symplectic group of rank \(n\)) has been the subject of a great deal of work; a survey of the history of this can be found in the introduction of this article.
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Kabirian-based optinalysis: A conceptually grounded framework for symmetry/asymmetry, similarity/dissimilarity and identity/unidentity estimations in mathematical structures and biological sequences. [PDF]
MethodsX, 2023 Abdullahi KB.
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