Since the 1930s, the analytic theory of numbers has been transformed by the influence of I. M. Vinogradov, and this text for upper-level undergraduates and graduate students testifies to its author's ingenuity and to the effectiveness of his methods. Starting with a discussion of general lemmas, it advances to an investigation of Waring's problem, including explorations of singular series, the contribution of the basic intervals, and an estimate for G(n). Further topics include approximation by the fractional parts of the values of a polynomial, estimates for Weyl sums, the asymptotic formula in Waring's problem, the distribution of the fractional parts of the values of a polynomial, estimates for the simplest trigonometrical sums with primes, and Goldbach's problem. 1954 edition.

The Method of Trigonometrical Sums in the Theory of Numbers (Dover Books on Mathematics)

Science & Math

MATHEMATICS

Vinogradov, I. M.

Mathematics

Dover Publications

"A very welcome addition to books on number theory."—Bulletin, American Mathematical SocietyClear and detailed in its exposition, this text can be understood by readers with no background in advanced mathematics; only a small part requires a working knowledge of calculus. One of the most valuable characteristics of this book is its stress on learning number theory by means of demonstrations and problems. More than 200 problems and full solutions appear in the text, plus 100 numerical exercises. Some of these exercises deal with estimation of trigonometric sums and are especially valuable as introductions to more advanced studies. Translation of 1949 Russian edition.

Elements of Number Theory

"A very welcome addition to books on number theory."—Bulletin, American Mathematical Society Clear and detailed in its exposition, this text can be understood by readers with no background in advanced mathematics; only a small part requires a working knowledge of calculus. One of the most valuable characteristics of this book is its stress on learning number theory by means of demonstrations and problems. More than 200 problems and full solutions appear in the text, plus 100 numerical exercises. Some of these exercises deal with estimation of trigonometric sums and are especially valuable as introductions to more advanced studies. Translation of 1949 Russian edition.

Elements of Number Theory (Dover Books on Mathematics)

Book by International Conference on Number Theory Moscow 1971, Vinogradov, I. M.

Proceedings of the International Conference on Number Theory (MOSCOW, SEPTEMBER 14-18, 1971) (English and Russian Edition)

International Conference on Number Theory Moscow 1971

Amer Mathematical Society

This book, dedicated to the 100th anniversary of the birth of I. M. Vinogradov, contains papers ranging over various areas of mathematics, including number theory, algebra, theory of functions of a real variable and of a complex variable, ordinary differential equations, optimal control, partial differential equations, mathematical physics, mechanics, and probability.

Number Theory, Algebra, Mathematical Analysis, and Their Applications: Dedicated to the 100th Anniversary of the Birth of Ivan Matveevich Vinogradov ... of the Steklov Institute of Mathematics)

Vladimirov, V. S.