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1998 Quadratic minima and modular forms
Barry Brent
Experiment. Math. 7(3): 257-274 (1998).

Abstract

We give upper bounds on the size of the gap between the constant term and the next nonzero Fourier coefficient of an entire modular form of given weight for $\flop{L}{-.3}\!_0(2)$. Numerical evidence indicates that a sharper bound holds for the weights $h \equiv 2 \pmod 4$. We derive upper bounds for the minimum positive integer represented by level-two even positive-definite quadratic forms. Our data suggest that, for certain meromorphic modular forms and $p=2$, $3$, the $p$-order of the constant term is related to the base-$p$ expansion of the order of the pole at infinity.

Citation

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Barry Brent. "Quadratic minima and modular forms." Experiment. Math. 7 (3) 257 - 274, 1998.

Information

Published: 1998
First available in Project Euclid: 14 March 2003

zbMATH: 0916.11025
MathSciNet: MR1676754

Subjects:
Primary: 11F30
Secondary: 11E25

Rights: Copyright © 1998 A K Peters, Ltd.

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Vol.7 • No. 3 • 1998
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