Functiones et Approximatio Commentarii Mathematici

A note on the extended Bruinier-Kohnen conjecture

Mohammed Amin Amri and M'hammed Ziane

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Abstract

Let $f$ be a cusp form of half-integral weight $k+1/2$, whose Fourier coefficients $a(n)$ are not necessarily real. We prove an extension of the Bruinier-Kohnen conjecture on the equidistribution of the signs of $a(n)$ for the families $\{a(tp^{2\nu})\}_{p,\text{prime}}$, where $\nu$ and $t$ be fixed odd positive integer and square-free integer respectively.

Article information

Source
Funct. Approx. Comment. Math., Volume 61, Number 2 (2019), 139-146.

Dates
First available in Project Euclid: 26 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.facm/1572055487

Digital Object Identifier
doi:10.7169/facm/1723

Mathematical Reviews number (MathSciNet)
MR4042387

Zentralblatt MATH identifier
07149353

Subjects
Primary: 11F03: Modular and automorphic functions 11F30: Fourier coefficients of automorphic forms 11F37: Forms of half-integer weight; nonholomorphic modular forms

Keywords
sign changes Fourier coefficients of cusp forms Sato-Tate equidistribution

Citation

Amri, Mohammed Amin; Ziane, M'hammed. A note on the extended Bruinier-Kohnen conjecture. Funct. Approx. Comment. Math. 61 (2019), no. 2, 139--146. doi:10.7169/facm/1723. https://projecteuclid.org/euclid.facm/1572055487


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References

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