On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen conjecture
TURKISH JOURNAL OF MATHEMATICS, cilt.45, ss.2427-2440, 2021 (SCI-Expanded, TRDizin)
- 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.