Linear sums and the Gaussian multiplication theorem

O. V. Kolpakova, V. N. Chubarikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Estimations of linear sums with Bernoulli polynomial of the first degree are given. If the coefficient of the linear function is a irrational number with the bounded partial quotients, the arithmetical sum has the “squaring” estimation. The Roth's theorem gives the similar estimation for all algebraic number, but the constants in estimations be nonefficient. New difficulties appears for sums over primes. Their are connected with the consideration of bilinear forms.
Bibliography: 24 titles.

Keywords: arithmetical sums, the Gaussian multiplication theorem for the Euler's Gamma-function, the functional theorem of the Gaussian type, the Bernoulli polynomials, algebraic numbers, arithmetical sums over primes, the Roth's theorem.

UDC: 511.3

Received: 08.12.2015
Accepted: 10.03.2016

Bibliographic databases:

•