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

İNAM İ., Özkaya Z. D., Tercan E., Wiese G.

Turkish Journal of Mathematics, vol.45, no.6, pp.2427-2440, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2105-40
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2427-2440
  • Keywords: Distribution of coefficients, Fourier coefficients of automorphic forms, Modular forms of half-integer weight, Ramanujan–Petersson conjecture, Sato–Tate conjecture, Sign changes
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2021This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level Γ0(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.