Half-integral weight modular forms and real quadratic $p$-rational fields

Jilali Assim; Zakariae Bouazzaoui

doi:10.7169/facm/1851

Abstract

Using half-integral weight modular forms we give a criterion for the existence of real quadratic $p$-rational fields. For $p=5$ we prove the existence of infinitely many real quadratic $p$-rational fields.

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Jilali Assim. Zakariae Bouazzaoui. "Half-integral weight modular forms and real quadratic $p$-rational fields." Funct. Approx. Comment. Math. 63 (2) 201 - 213, December 2020. https://doi.org/10.7169/facm/1851

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Published: December 2020

First available in Project Euclid: 8 May 2020

MathSciNet: MR4184272

Digital Object Identifier: 10.7169/facm/1851

Subjects:

Primary: 11R11

Secondary: 11F37 , 11R42

Keywords: $L$-functions , $p$-rational fields , modular forms

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