Half-integral weight p-adic coupling of weakly holomorphic and holomorphic modular forms [PDF]
Research in Number Theory, 2015 In this paper, we consider p-adic limits of β−ng|Up2n$\beta ^{-n}g|U_{p^{2}}^{n}$ for half-integral weight weakly holomorphic Hecke eigenforms g with eigenvalue λp=β+β′ under Tp2$T\phantom {\dot {i}\!}_{p^{2}}$ and prove that these equal classical Hecke ...
Kathrin Bringmann +2 more
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On coefficients of Poincaré series and single-valued periods of modular forms. [PDF]
Res Math Sci, 2020 We prove that the field generated by the Fourier coefficients of weakly holomorphic Poincaré series of a given level Γ0(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage ...
Fonseca TJ.
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Weakly holomorphic modular forms of half-integral weight with nonvanishing constant terms modulo $\ell $ [PDF]
, 2009 Dong‐Soo Choi
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Skew-holomorphic Jacobi forms of index 1 and Siegel modular forms of half-integral weight
, 2004 Shuichi Hayashida
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Nonzero coefficients of half-integral weight modular forms mod $$\ell $$ℓ [PDF]
Research in the Mathematical Sciences, 2017 We obtain new lower bounds for the number of Fourier coefficients of a weakly holomorphic modular form of half-integral weight not divisible by some prime $$\ell $$ℓ.
J. Bellaïche +2 more
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Zeros of modular forms of half integral weight [PDF]
Research in Number Theory, 2016 We study canonical bases for spaces of weakly holomorphic modular forms of level 4 and weights in $$\mathbb {Z}+\frac{1}{2}$$Z+12 and show that almost all modular forms in these bases have the property that many of their zeros in a fundamental domain for
A. Folsom, P. Jenkins
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Scalar‐valued depth two Eichler–Shimura integrals of cusp forms
Transactions of the London Mathematical Society, 2023 Given cusp forms f and g of integral weight k⩾2, the depth two holomorphic iterated Eichler–Shimura integral If,g is defined by ∫τi∞f(z)(X−z)k−2Ig(z;Y)dz, where Ig is the Eichler integral of g and X,Y are formal variables.
Tobias Magnusson, Martin Raum
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A class of non-holomorphic modular forms III: real analytic cusp forms for $$\mathrm {SL}_2(\mathbb {Z})$$SL2(Z) [PDF]
Research in the Mathematical Sciences, 2017 We define canonical real analytic versions of modular forms of integral weight for the full modular group, generalising real analytic Eisenstein series. They are harmonic Maass waveforms with poles at the cusp, whose Fourier coefficients involve periods ...
F. Brown
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Fourier Coefficients of Modular Forms of Half-Integral Weight in Arithmetic Progressions [PDF]
International mathematics research notices, 2019 We study the probabilistic behavior of sums of Fourier coefficients in arithmetic progressions. We prove a result analogous to previous work of Fouvry–Ganguly–Kowalski–Michel and Kowalski–Ricotta in the context of half-integral weight holomorphic cusp ...
Corentin Darreye
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Shimura lifts of weakly holomorphic modular forms [PDF]
Mathematische Zeitschrift, 2017 We show how to realize the Shimura lift of arbitrary level and character using the vector-valued theta lifts of Borcherds. Using the regularization of Borcherds’ lift we extend the Shimura lift to take weakly holomorphic modular forms of half-integral ...
Yingkun Li, Shaul Zemel
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