LINEAR SUMS AND THE GAUSSIAN MULTIPLICATION THEOREM
https://doi.org/10.22405/2226-8383-2016-17-1-130-139
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, thearithmetical 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.
About the Authors
O. V. Kolpakova
Lomonosov Moscow State University
Russian Federation
Russian Federation
Candidate of Physico-Mathematical Sciences, Associate Professor
V. N. Chubarikov
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor, head of the Department of mathematical and computer methods of analysis, dean of the mechanics and mathematics faculty of the M. V.
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Review
For citations:
Kolpakova O.V., Chubarikov V.N. LINEAR SUMS AND THE GAUSSIAN MULTIPLICATION THEOREM. Chebyshevskii Sbornik. 2016;17(1):130-139. (In Russ.) https://doi.org/10.22405/2226-8383-2016-17-1-130-139
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