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1997 Non-ordinary primes: a story
Fernando Q. Gouvêa
Experiment. Math. 6(3): 195-205 (1997).

Abstract

A normalized modular eigenform f is said to be ordinary at a prime p if p does not divide the p-th Fourier coefficient of f. We take f to be a modular form of level $1$ and weight $k\in\{12$,$\,16$,$\,18$,$\,20$,$\,22$,$\,26\}$ and search for primes where f is not ordinary. To do this, we need an efficient way to compute the reduction modulo p of the p-th Fourier coefficient. A convenient formula was known for $k=12$; trying to understand it leads to generalized Rankin-Cohen brackets and thence to formulas that we can use to look for non-ordinary primes. We do this for $p\leq 1\,000\,000$.

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Fernando Q. Gouvêa. "Non-ordinary primes: a story." Experiment. Math. 6 (3) 195 - 205, 1997.

Information

Published: 1997
First available in Project Euclid: 17 March 2003

zbMATH: 0887.11020
MathSciNet: MR1481589

Subjects:
Primary: 11F11
Secondary: 11F25 , 11F30 , 11Y35

Rights: Copyright © 1997 A K Peters, Ltd.

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Vol.6 • No. 3 • 1997
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