On the distribution of coeﬀicients of half-integral weight modular forms and the Bruinier–Kohnen conjecture

İlker Inam, Zeynep DEMİRKOL ÖZKAYA, Elif TERCAN, Gabor Wiese

Type: Article

Publication Date: 2021-08-24

Citations: 3

DOI: https://doi.org/10.3906/mat-2105-40

Abstract

This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level $\Gamma_0(4)$ and half-integral weights. Based on substantial calculations, the question is raised whether the distribution of normalised Fourier coefficients with bounded indices can be approximated by a generalised Gaussian distribution. Moreover, it is argued that the apparent symmetry around zero of the data lends strong evidence to the Bruinier-Kohnen Conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently.

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TURKISH JOURNAL OF MATHEMATICS - View - PDF
arXiv (Cornell University) - View - PDF
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Works Cited by This (43)

Action	Title	Year	Authors
+	Sur les coefficients de Fourier des formes modulaires de poids demi-entier	1981	J. L. Waldspurger
+	Sign changes of coefficients of half integral weight modular forms	2007	Jan Hendrik Bruinier Winfried Kohnen
+	Nonvanishing of Fourier coefficients of modular forms	2002	Emre Alkan
+	A note on small gaps between nonzero Fourier coefficients of cusp forms	2015	Soumya Das Satadal Ganguly
+ PDF Chat	Oscillations of Fourier coefficients of modular forms	1983	M. Ram Murty
+	The Magma Algebra System I: The User Language	1997	Wieb Bosma John Cannon Catherine Playoust
+ PDF Chat	Nonvanishing of Fourier coefficients of newforms in progressions	2005	Emre Alkan Alexandru Zaharescu
+	Values ofL-series of modular forms at the center of the critical strip	1981	Winfried Kohnen Don Zagier
+	Diophantine approximation with arithmetic functions, I	2008	Emre Alkan Kevin Ford Alexandru Zaharescu
+	The first sign change of Fourier coefficients of cusp forms	2009	YoungJu Choie Winfried Kohnen