Large Fourier coefficients of half-integer weight modular forms

• Verfasst von: Gun, Sanoli [VerfasserIn]
• Verfasst von: Kohnen, Winfried [VerfasserIn]
• Verfasst von: Soundararajan, Kannan [VerfasserIn]
• Titel: Large Fourier coefficients of half-integer weight modular forms
• Verf.angabe: by S. Gun, W. Kohnen, and K. Soundararajan
• Jahr: 2024
• Umfang: 23 S.
• Fussnoten: Gesehen am 21.02.2025
• Titel Quelle: Enthalten in: American journal of mathematics
• Ort Quelle: Baltimore, Md. : Johns Hopkins Univ. Press, 1878
• Jahr Quelle: 2024
• Band/Heft Quelle: 146(2024), 4, Seite 1169-1191
• ISSN Quelle: 1080-6377
• DOI: doi:10.1353/ajm.2024.a932437
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: EXTREME VALUES
• Sach-SW: SUMS
• Sach-SW: TWISTS
• K10plus-PPN: 191775745X

Abstract

This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants D such that the Fourier coefficients evaluated at D are non-zero. By adapting the resonance method, we also demonstrate that such Fourier coefficients must take quite large values.