Estimates on exponential sums - Open Access .click

Forum Mathematicum, 2014
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 estimates on average over arithmetic progressions are obtained.
Louvel, Benoit
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The Estimation of Complete Exponential Sums

Canadian Mathematical Bulletin, 1985
AbstractThis paper proves a conjecture of Loxton and Smith about the size of the exponential sum S(f;q) formed by summing exp (2πif(x)/q) over x mod q, where f is a polynomial of degree n with integer coefficients. It is shown that |S(f;q)| ≤ Cfdn(q)qe/(e+1), where e is the maximum of the orders of the complex zeros of f'.
Loxton, J. H., Vaughan, R. C.
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Exponential estimates for the maximum of partial sums. I

Acta Mathematica Hungarica, 1979
F Mòricz
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An Application of Exponential Sum Estimates

Acta Mathematica Sinica, English Series, 2004
Let \(p\) be an odd prime, \(\delta\) a fixed real with \(0 < \delta < 2\), and \(k, l\) fixed positive integers. Let \(N_{k, l}(p, \delta)\) denote the number of solutions of the inequality \[ \left| \left\{ a^k/p \right\} + \left\{ b^k/p \right\} - \left\{ \bar a^l/p \right\} - \left\{ \bar b^l/p \right\} \right| < \delta \] in \(a, b \in \mathbb F_p^
Yi, Yuan, Zhang, Wenpeng
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exponential sums
estimates on character sums
exponential sum

gauss and kloosterman sums generalizations
fos: mathematics
mathematics - number theory

number theory math.nt
estimate
11l07