Sign changes of Fourier coefficients of cusp forms of half-integral weight over split and inert primes in quadratic number fields

DOI10.1007/S40993-020-00235-9zbMATH Open1460.11063arXiv2004.00578OpenAlexW3119212989MaRDI QIDQ2221700

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Publication date: 2 February 2021

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Abstract: In this paper, we investigate sign changes of Fourier coefficients of half-integral weight cusp forms. In a fixed square class $tmathbb{Z}^2$, we investigate the sign changes in the $t{p}^2$-th coefficient as $p$ runs through the split or inert primes over the ring of integers in a quadratic extension of the rationals. We show that sign changes occur in both sets of primes when there exists a prime dividing the discriminant of the field which does not divide the level of the cusp form and find an explicit condition that determines whether sign changes occur when every prime dividing the discriminant also divides the level.

Full work available at URL: https://arxiv.org/abs/2004.00578

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