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

İNAM, İlker; TERCAN, Elif; Demirkol Özkaya, Zeynep; Wiese, Gabor

doi:10.3906/mat-2105-40

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

İlker İNAM, (Bilecik Şeyh Edebali Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, Bilecik, Türkiye)

Zeynep DEMİRKOL ÖZKAYA, (Van Yüzüncüyıl Üniversitesi, Muradiye Meslek Yüksekokulu, Van, Türkiye)

Elif TERCAN, (Bilecik Şeyh Edebali Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, Bilecik, Türkiye)

Gabor WIESE (Department of Mathematics, University of Luxembourg, Esch-sur-Alzette, Luxembourg)

Turkish Journal of Mathematics

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Yıl: 2021 Cilt: 45 Sayı: 6 Sayfa Aralığı: 2427 - 2440 Metin Dili: İngilizce DOI: 10.3906/mat-2105-40 İndeks Tarihi: 01-07-2022

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

Öz:

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.

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APA	İNAM İ, Demirkol Özkaya Z, TERCAN E, Wiese G (2021). On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. , 2427 - 2440. 10.3906/mat-2105-40
Chicago	İNAM İlker,Demirkol Özkaya Zeynep,TERCAN Elif,Wiese Gabor On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. (2021): 2427 - 2440. 10.3906/mat-2105-40
MLA	İNAM İlker,Demirkol Özkaya Zeynep,TERCAN Elif,Wiese Gabor On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. , 2021, ss.2427 - 2440. 10.3906/mat-2105-40
AMA	İNAM İ,Demirkol Özkaya Z,TERCAN E,Wiese G On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. . 2021; 2427 - 2440. 10.3906/mat-2105-40
Vancouver	İNAM İ,Demirkol Özkaya Z,TERCAN E,Wiese G On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. . 2021; 2427 - 2440. 10.3906/mat-2105-40
IEEE	İNAM İ,Demirkol Özkaya Z,TERCAN E,Wiese G "On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture." , ss.2427 - 2440, 2021. 10.3906/mat-2105-40
ISNAD	İNAM, İlker vd. "On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture". (2021), 2427-2440. https://doi.org/10.3906/mat-2105-40

APA	İNAM İ, Demirkol Özkaya Z, TERCAN E, Wiese G (2021). On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. Turkish Journal of Mathematics, 45(6), 2427 - 2440. 10.3906/mat-2105-40
Chicago	İNAM İlker,Demirkol Özkaya Zeynep,TERCAN Elif,Wiese Gabor On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. Turkish Journal of Mathematics 45, no.6 (2021): 2427 - 2440. 10.3906/mat-2105-40
MLA	İNAM İlker,Demirkol Özkaya Zeynep,TERCAN Elif,Wiese Gabor On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. Turkish Journal of Mathematics, vol.45, no.6, 2021, ss.2427 - 2440. 10.3906/mat-2105-40
AMA	İNAM İ,Demirkol Özkaya Z,TERCAN E,Wiese G On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. Turkish Journal of Mathematics. 2021; 45(6): 2427 - 2440. 10.3906/mat-2105-40
Vancouver	İNAM İ,Demirkol Özkaya Z,TERCAN E,Wiese G On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture. Turkish Journal of Mathematics. 2021; 45(6): 2427 - 2440. 10.3906/mat-2105-40
IEEE	İNAM İ,Demirkol Özkaya Z,TERCAN E,Wiese G "On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture." Turkish Journal of Mathematics, 45, ss.2427 - 2440, 2021. 10.3906/mat-2105-40
ISNAD	İNAM, İlker vd. "On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture". Turkish Journal of Mathematics 45/6 (2021), 2427-2440. https://doi.org/10.3906/mat-2105-40