On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen conjecture
TURKISH JOURNAL OF MATHEMATICS, vol.45, pp.2427-2440, 2021 (SCI-Expanded, TRDizin)
- Publication Type: Article / Article
- Volume: 45
- Publication Date: 2021
- Doi Number: 10.3906/mat-2105-40
- Journal Name: TURKISH JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), TR DİZİN (ULAKBİM)
- Page Numbers: pp.2427-2440
- Keywords: Modular forms of half-integer weight, Fourier coefficients of automorphic forms, Ramanujan-Petersson conjecture, Sato-Tate conjecture, distribution of coefficients, sign changes, FOURIER COEFFICIENTS, VALUES, GAPS
- Van Yüzüncü Yıl University Affiliated: Yes
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.