Sum-product estimates applied to Waring's problem mod .
On representing the multiple of a number by a quadratic form
Exponential sums modulo prime powers
Exponential sums with rational function entries
Pure and mixed exponential sums
Lattices in ℤ² and the congruence xy+uv ≡ c(mod m)
Strong Riesz sets and polynomials
A system of simultaneous congruences arising from trinomial exponential sums
For a prime and positive integers with , we show that , the number of simultaneous solutions in to , , , satisfies When we obtain a precise asymptotic count on . This leads to the new twisted exponential sum bound for trinomials , and to results on the average size of such sums.
Sparse polynomial exponential sums
A further refinement of Mordell's bound on exponential sums
On the parity of k-th powers modulo p. A generalization of a problem of Lehmer
Waring's number for large subgroups of ℤ*ₚ*
Let p be a prime, ℤₚ be the finite field in p elements, k be a positive integer, and A be the multiplicative subgroup of nonzero kth powers in ℤₚ. The goal of this paper is to determine, for a given positive integer s, a value tₛ such that if |A| ≫ tₛ then every element of ℤₚ is a sum of s kth powers. We obtain , and for s ≥ 6, . For s ≥ 24 further improvements are made, such as and .
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