The Asymptotic Distribution of Exponential Sums, II
Patterson, S. J.
Experiment. Math., Tome 14 (2005) no. 1, p. 87-98 / Harvested from Project Euclid
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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.
Publié le : 2005-05-14
Classification:  Cubic exponential sums,  Kummer conjecture,  Gauss sums,  11L05 
@article{1120145573,
     author = {Patterson, S. J.},
     title = {The Asymptotic Distribution of Exponential Sums, II},
     journal = {Experiment. Math.},
     volume = {14},
     number = {1},
     year = {2005},
     pages = { 87-98},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1120145573}
}

Patterson, S. J. The Asymptotic Distribution of Exponential Sums, II. Experiment. Math., Tome 14 (2005) no. 1, pp.  87-98. http://gdmltest.u-ga.fr/item/1120145573/