TY  - JOUR
TI  - On the distribution of coefficients of half-integral weight modular forms and the
Bruinier–Kohnen conjecture
AB  - This 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.
AU  - İNAM, İlker
AU  - TERCAN, Elif
AU  - Demirkol Özkaya, Zeynep
AU  - Wiese, Gabor
DO  - 10.3906/mat-2105-40
PY  - 2021
JO  - Turkish Journal of Mathematics
VL  - 45
IS  - 6
SN  - 1300-0098
SP  - 2427
EP  - 2440
DB  - TRDizin
UR  - http://search/yayin/detay/528574
ER  -