Böcherer, S and Das, S (2022) On Fourier coefficients of elliptic modular forms modℓ with applications to Siegel modular forms. In: Manuscripta Mathematica, 167 (3-4). pp. 405-434.
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Abstract
We study several aspects of nonvanishing Fourier coefficients of elliptic modular forms modℓ, partially answering a question of Bellaïche-Soundararajan concerning the asymptotic formula for the count of the number of Fourier coefficients upto x which do not vanish modℓ. We also propose a precise conjecture as a possible answer to this question. Further, we prove several results related to the nonvanishing of arithmetically interesting (e.g., primitive or fundamental) Fourier coefficients modℓ of a Siegel modular form with integral algebraic Fourier coefficients provided ℓ is large enough. We also make some efforts to make this “largeness” of ℓ effective.
| Item Type: | Journal Article |
|---|---|
| Publication: | Manuscripta Mathematica |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 29 Jun 2022 06:19 |
| Last Modified: | 29 Jun 2022 06:19 |
| URI: | https://eprints.iisc.ac.in/id/eprint/73836 |
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