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Romik's conjecture for the Jacobi theta function.
- Source :
-
Journal of Number Theory . Oct2020, Vol. 215, p275-296. 22p. - Publication Year :
- 2020
-
Abstract
- Dan Romik recently considered the Taylor coefficients of the Jacobi theta function around the complex multiplication point i. He then conjectured that the Taylor coefficients d (n) either vanish or are periodic modulo any prime p ; this was proved by the combined efforts of Scherer and Guerzhoy-Mertens-Rolen, with the latter trio considering arbitrary half integral weight modular forms. We refine previous work for p ≡ 1 (mod 4) by displaying a concise algebraic relation between d (n + p − 1 2) and d (n) related to the p -adic factorial, from which we can deduce periodicity with an effective period. [ABSTRACT FROM AUTHOR]
- Subjects :
- *THETA functions
*MODULAR forms
*LOGICAL prediction
*NUMBER theory
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 215
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 144265710
- Full Text :
- https://doi.org/10.1016/j.jnt.2020.01.009