Abstract: This volume is dedicated to the 130th anniversary of the birth of the outstanding mathematician
Academician Ivan Matveevich Vinogradov. The volume includes a course of lectures (1983) by
A. A. Karatsuba on Vinogradov's life and work, as well as articles on various fields of analytic
number theory and additive combinatorics, such as methods for estimating exponential and character
sums, distribution of primes, universal properties of $L$-series, additive functions, Cayley
graphs, structure theorems, etc. Most of the articles are written by leading mathematicians in the
above fields.
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