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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 termand the next nonzero Fourier coefficient of an entire modular form ofgiven weight for $\flop{L}{-.3}\!_0(2)$. Numerical evidence indicates that asharper bound holds for the weights $h \equiv 2 \pmod 4$. We deriveupper bounds for the minimum positive integer represented by level-twoeven positive-definite quadratic forms. Our data suggest that, forcertain meromorphic modular forms and $p=2$, $3$, the $p$-order of theconstant term is related to the base-$p$ expansion of the order of thepole 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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