GUN, SANOLI ; RAM MURTY, M. ; RATH, PURUSOTTAM (2011) Algebraic Independence Of Values Of Modular Forms International Journal of Number Theory, 07 (04). pp. 1065-1074. ISSN 1793-0421
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Official URL: http://doi.org/10.1142/S1793042111004769
Related URL: http://dx.doi.org/10.1142/S1793042111004769
Abstract
We investigate values of modular forms with algebraic Fourier coefficients at algebraic arguments. As a consequence, we conclude about the nature of zeros of such modular forms. In particular, the singular values of modular forms (that is, values at CM points) are related to the recent work of Nesterenko. As an application, we deduce the transcendence of critical values of certain Hecke L-series. We also discuss how these investigations generalize to the case of quasi-modular forms with algebraic Fourier coefficients.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to World Scientific Publishing Co Pte Ltd. |
| Keywords: | Transcendental Values Of Modular Forms; Schneider's Theorem; Nesterenko's Theorem. |
| ID Code: | 117993 |
| Deposited On: | 10 May 2021 13:02 |
| Last Modified: | 10 May 2021 13:02 |
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