Twisted exponential sums over points of elliptic curves
Twists and resonance of -functions, I
We obtain the basic analytic properties, i.e. meromorphic continuation, polar structure and bounds for the order of growth, of all the nonlinear twists with exponents of the -functions of any degree in the extended Selberg class. In particular, this solves the resonance problem in all such cases.
Un Théoreme de Moyenne Pour les Sommes D'exponentielles. Application a L'inégalité de Weyl
Vergleich der unterschiedlichen Gütemaße zur Bewertung von Auto- und Kreuzkorrelationsfunktionen
Vinogradov's exponential sum over primes
Vinogradov's mean value theorem.
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 .
О некоторых задачах геометрии простых чисел
О распределении знаков в периодических дробях