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We give a congruence for L-functions coming from affine additive exponential sums over a finite field. Precisely, we give a congruence for certain operators coming from Dwork's theory. This congruence...
On Character Sums and Exponential Sums over Generalized Arithmetic Progressions
Character Sums Exponential Sums Generalized Arithmetic Progressions Number Theory
2012/6/19
We study upper bounds for sums of Dirichlet characters. We prove a uniform upper bound of the character sum over all proper generalized arithmetic progressions, which generalizes the classical Polya a...
L^2-norms of exponential sums over prime powers
Primes in short intervals Diophantine problems with primes Number Theory
2012/6/14
We study a suitable mean-square average of primes in short intervals, generalizing Saffari-Vaughan's result. We then apply it to a ternary Diophantine problem with prime variables.
On the distribution of cubic exponential sums
Exponential sums Cubic theta functions Metaplectic forms
2011/8/23
Abstract: Using the theory of metaplectic forms,we study the asymptotic behavior of cubic exponential sums over the ring of Eisenstein integers. In the first part of the paper, some non-trivial estima...
On unit root formulas for toric exponential sums
Exponential sum A-hypergeometric function
2011/1/19
Starting from a classical generating series for Bessel functions due to Schl¨omilch[4], we use Dwork’s relative dual theory to broadly generalize unit-root results of Dwork[3] on Kloosterman sums and ...