The Experts below are selected from a list of 41322 Experts worldwide ranked by ideXlab platform
René Olivetto - One of the best experts on this subject based on the ideXlab platform.
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On the Fourier Coefficients of meromorphic Jacobi forms
International Journal of Number Theory, 2014Co-Authors: René OlivettoAbstract:In this paper, we describe the automorphic properties of the Fourier Coefficients of meromorphic Jacobi forms. Extending results of Dabholkar, Murthy, and Zagier, and Bringmann and Folsom, we prove that the canonical Fourier Coefficients of a meromorphic Jacobi form φ(z; τ) are the holomorphic parts of some (vector-valued) almost harmonic Maass forms. We also give a precise description of their completions, which turn out to be uniquely determined by the Laurent Coefficients of φ at each pole, as well as some well-known real analytic functions, that appear for instance in the completion of Appell–Lerch sums.
Winfried Kohnen - One of the best experts on this subject based on the ideXlab platform.
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On sign changes of Fourier Coefficients of modular forms
Research in Number Theory, 2018Co-Authors: Winfried Kohnen, Yichao ZhangAbstract:It is known that if a nonzero cusp form has real Fourier Coefficients, then its Fourier Coefficients change signs infinitely often. In this paper, we prove that there is a codimension one subspace in the space of holomorphic modular forms of square-free level such that all of its non-zero forms have similar sign change property.
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On Products of Fourier Coefficients of Cusp Forms
Forum Mathematicum, 2017Co-Authors: Eric Hofmann, Winfried KohnenAbstract:The purpose of this paper is to study products of Fourier Coefficients of an elliptic cusp form, $a(n)a(n + r)$ $(n \geq 1)$ for a fixed positive integer $r$, concerning both non-vanishing and non-negativity.
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Simultaneous sign change of Fourier-Coefficients of two cusp forms
Archiv der Mathematik, 2015Co-Authors: Sanoli Gun, Winfried Kohnen, Purusottam RathAbstract:We consider the simultaneous sign change of Fourier Coefficients of two modular forms with real Fourier Coefficients. In an earlier work, the second author with Sengupta proved that two cusp forms of different (integral) weights with real algebraic Fourier Coefficients have infinitely many Fourier Coefficients of the same as well as opposite sign, up to the action of a Galois automorphism. In the first part, we strengthen their result by doing away with the dependency on the Galois conjugacy. In fact, we extend their result to cusp forms with arbitrary real Fourier Coefficients. Next we consider simultaneous sign change at prime powers of Fourier Coefficients of two integral weight Hecke eigenforms which are newforms. Finally, we consider an analogous question for Fourier Coefficients of two half-integral weight Hecke eigenforms.
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Fourier Coefficients and Hecke eigenvalues
Nagoya Mathematical Journal, 1998Co-Authors: Winfried KohnenAbstract:We will give certain asymptotic relations between p -eigenvalues and certain Fourier Coefficients of Siegel cusp forms of genus g . In particular, it will turn out that potential strong bounds for the Fourier Coefficients will imply potential strong bounds for the eigenvalues.
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Estimates for Fourier Coefficients of Siegel cusp forms
Mathematische Annalen, 1993Co-Authors: Siegfried Böcherer, Winfried KohnenAbstract:The proof of (1) was based on appropriate estimates both for the Fourier Coefficients of cusp forms on the Jacobi group F1 ~' 2. More precisely, let
Wissam Raji - One of the best experts on this subject based on the ideXlab platform.
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Fourier Coefficients of generalized modular forms of negative weight
International Journal of Number Theory, 2009Co-Authors: Wissam RajiAbstract:The Fourier Coefficients of classical modular forms of negative weights have been determined for the case for which F(τ) belongs to a subgroup of the full modular group [9]. In this paper, we determine the Fourier Coefficients of generalized modular forms of negative weights using the circle method.
Sander Zwegers - One of the best experts on this subject based on the ideXlab platform.
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on the Fourier Coefficients of negative index meromorphic jacobi forms
arXiv: Number Theory, 2015Co-Authors: Kathrin Bringmann, Larry Rolen, Sander ZwegersAbstract:In this paper, we consider the Fourier Coefficients of meromorphic Jacobi forms of negative index. This extends recent work of Creutzig and the first two authors for the special case of Kac-Wakimoto characters which occur naturally in Lie theory, and yields, as easy corollaries, many important PDEs arising in combinatorics such as the famous rank-crank PDE of Atkin and Garvan. Moreover, we discuss the relation of our results to partial theta functions and quantum modular forms as introducted by Zagier, which together with previous work on positive index meromorphic Jacobi forms illuminates the general structure of the Fourier Coefficients of meromorphic Jacobi forms.
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Fourier Coefficients of meromorphic Jacobi forms
2015Co-Authors: Sander ZwegersAbstract:Fourier Coefficients of meromorphic Jacobi forms show up in, for example, the study of mock theta functions, quantum black holes and Kac-Wakimoto characters. In the case of positive index, it was previously shown that they are the holomorphic parts of vector-valued almost harmonic Maass forms. In this talk, we give an alternative characterization of these objects by applying the Maass lowering operator to the completions of the Fourier Coefficients. Further, we'll also describe the relation of Fourier Coefficients of negative index Jacobi forms to partial theta functions.
Goran Muic - One of the best experts on this subject based on the ideXlab platform.
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Fourier Coefficients of automorphic forms and integrable discrete series
Journal of Functional Analysis, 2016Co-Authors: Goran MuicAbstract:Abstract Let G be the group of R -points of a semisimple algebraic group G defined over Q . Assume that G is connected and noncompact. We study Fourier Coefficients of Poincare series attached to matrix Coefficients of integrable discrete series. We use these results to construct explicit automorphic cuspidal realizations, which have appropriate Fourier Coefficients ≠0, of integrable discrete series in families of congruence subgroups. In the case of G = Sp 2 n ( R ) , we relate our work to that of Li [14] . For G quasi-split over Q , we relate our work to the result about Poincare series due to Khare, Larsen, and Savin [12] .
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Fourier Coefficients of automorphic forms and integrable discrete series
arXiv: Number Theory, 2015Co-Authors: Goran MuicAbstract: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. We use these results to construct explicit automorphic cuspidal realizations, which have appropriate Fourier Coefficients $\neq 0$, of integrable discrete series in families of congruence subgroups. In the case of $G=Sp_{2n}(\mathbb R)$, we relate our work to that of Li [15]. For $\mathcal G$ quasi--split over $\mathbb Q$, we relate our work to the result about Poincar\' e series due to Khare, Larsen, and Savin [16].