Large Fourier coefficients of half-integer weight modular forms
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 adapti...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2024
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| In: |
American journal of mathematics
Year: 2024, Volume: 146, Issue: 4, Pages: 1169-1191 |
| ISSN: | 1080-6377 |
| DOI: | 10.1353/ajm.2024.a932437 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1353/ajm.2024.a932437 Verlag, lizenzpflichtig, Volltext: https://www.webofscience.com/api/gateway?GWVersion=2&SrcAuth=DOISource&SrcApp=WOS&KeyAID=10.1353%2Fajm.2024.a932437&DestApp=DOI&SrcAppSID=EUW1ED0F599i3zEC3pV2OdtcSC1sN&SrcJTitle=AMERICAN+JOURNAL+OF+MATHEMATICS&DestDOIRegistrantName=Project+MUSE 
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| Author Notes: | by S. Gun, W. Kohnen, and K. Soundararajan |
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| 520 | |a 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. | ||
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