Fourier coefficients of modular forms of half-integral weight

1987 ◽  
Vol 87 (2) ◽  
pp. 385-401 ◽  
Author(s):  
Henryk Iwaniec
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Half Integral Weight ◽  
Integral Weight

ARITHMETIC TRACES OF NON-HOLOMORPHIC MODULAR INVARIANTS

2010 ◽  
Vol 06 (01) ◽  
pp. 69-87 ◽  
Author(s):  
ALISON MILLER ◽  
AARON PIXTON
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Algebraic Numbers ◽  
Heegner Points ◽  
Positive Weight ◽  
Poincare Series ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Modular Invariants

We extend results of Bringmann and Ono that relate certain generalized traces of Maass–Poincaré series to Fourier coefficients of modular forms of half-integral weight. By specializing to cases in which these traces are usual traces of algebraic numbers, we generalize results of Zagier describing arithmetic traces associated to modular forms. We define correspondences [Formula: see text] and [Formula: see text]. We show that if f is a modular form of non-positive weight 2 - 2 λ and odd level N, holomorphic away from the cusp at infinity, then the traces of values at Heegner points of a certain iterated non-holomorphic derivative of f are equal to Fourier coefficients of the half-integral weight modular forms [Formula: see text].

Fourier Coefficients of Modular Forms of Half-Integral Weight in Arithmetic Progressions

2020 ◽  
Author(s):  
Corentin Darreye
Keyword(s):  
Gaussian Distribution ◽  
Modular Forms ◽  
Prime Power ◽  
Fourier Coefficients ◽  
Arithmetic Progressions ◽  
Cusp Forms ◽  
Half Integral Weight ◽  
Mixed Distribution ◽  
Integral Weight ◽  
Holomorphic Cusp Forms

Abstract 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 forms and for prime power modulus. We actually show that these sums follow in a suitable range a mixed Gaussian distribution that comes from the asymptotic mixed distribution of Salié sums.

scholarly journals On the algebraicity of coefficients of half-integral weight mock modular forms

2018 ◽  
Vol 16 (1) ◽  
pp. 1335-1343
Author(s):  
SoYoung Choi ◽  
Chang Heon Kim
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Mock Modular Forms ◽  
Half Integral Weight ◽  
Integral Weight

AbstractExtending works of Ono and Boylan to the half-integral weight case, we relate the algebraicity of Fourier coefficients of half-integral weight mock modular forms to the vanishing of Fourier coefficients of their shadows.

scholarly journals A note on the Fourier coefficients of half-integral weight modular forms

2014 ◽  
Vol 102 (4) ◽  
pp. 369-378 ◽  
Author(s):  
Narasimha Kumar ◽  
Soma Purkait
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Half Integral Weight ◽  
Integral Weight
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