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1998 Asymptotic formulas and generalized Dedekind sums
Gert Almkvist
Experiment. Math. 7(4): 343-359 (1998).

Abstract

We find asymptotic formulas as $n\to\infty$ for the coefficients $a(r\hbox{,}\,n)$ defined by $$ \prod_{\nu=1}^\infty\,(1-x^\nu)^{-\nu^r} =\sum_{n=0}^\infty a(r\hbox{,}\,n)x^n\hbox{.} $$ (The case $r=1$ gives the number of plane partitions of $n$.) Generalized Dedekind sums occur naturally and are studied using the Finite Fourier Transform. The methods used are unorthodox; many of the computations are not justified but the result is in many cases very good numerically. The last section gives various formulas for Kinkelin's constant.

Citation

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Gert Almkvist. "Asymptotic formulas and generalized Dedekind sums." Experiment. Math. 7 (4) 343 - 359, 1998.

Information

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

zbMATH: 0922.11083
MathSciNet: MR1678083

Subjects:
Primary: 11P82
Secondary: 11F20

Rights: Copyright © 1998 A K Peters, Ltd.

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Vol.7 • No. 4 • 1998
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