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2005 The Asymptotic Distribution of Exponential Sums, II
S. J. Patterson
Experiment. Math. 14(1): 87-98 (2005).

Abstract

Let $f(x)$ be a polynomial with integral coefficients and let, for $c>0$, $S(f(x),c)=\sum_{j \!\! \pmod c} \exp(2\pi\imath\frac{f(j)}c)$. If $f$ is a cubic polynomial then it is expected that $\sum_{c\le X} S(f(x),c) \sim k(f)X^{4/3}$. In this paper, we consider the special case $f(x)=Ax^3+Bx$ and propose a precise formula for $k(f)$. This conjecture represents a refined version of the classical Kummer conjecture.

Citation

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S. J. Patterson. "The Asymptotic Distribution of Exponential Sums, II." Experiment. Math. 14 (1) 87 - 98, 2005.

Information

Published: 2005
First available in Project Euclid: 30 June 2005

zbMATH: 1148.11043
MathSciNet: MR2146522

Subjects:
Primary: 11L05

Keywords: Cubic exponential sums , Gauss sums , Kummer conjecture

Rights: Copyright © 2005 A K Peters, Ltd.

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