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

Inam I., Demirkol Özkaya Z., Tercan E., Wiese G.

TURKISH JOURNAL OF MATHEMATICS, cilt.45, ss.2427-2440, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2105-40
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2427-2440
  • Anahtar Kelimeler: 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 Üniversitesi Adresli: Evet

Özet

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.