Selected Works: Prepared by the Steklov Mathematical Institute of the Academy of Sciences of the USSR on the Occasion of His Ninetieth

ISBN-13: 9783642553806 / Angielski / Miękka / 2014 / 401 str.

I. M. Vinogradov; L. D. Faddeev; R. V. Gamkrelidze

Opis

Springer-Verlag has invited me to bring out my Selected Works. Being aware that Springer-Verlag enjoys high esteem in the scientific world as a reputed publisher, I have willingly accepted the offer. Immediately, I was faced with two problems. The first was that of acquaint ing the reader with the important stages in my scientific aetivities. For this purpose, I have included in the Selected Works eertain of my early works that have greatly influeneed my later studies. For the same reason, I have also in cluded in the book those works that contain the first, erude versions of the proofs for many of my basic theorems. The second problem was that of giving the reader the best possible opportunity to familiarize himself with the most important results and to learn to use my method. For this reason I have included the later improved versions of the proofs for my basic results, as weil as the monographs The Method of Trigo nometric Sums in Number Theory (Seeond Edition) and Special Variants of the Method of Trigonometric Sums."

Spis treści

A New Method of Deriving Asymptotic Expressions for Arithmetic Functions.- On the Mean Value of the Number of Classes of Proper Primitive Forms of Negative Discriminant.- On the Distribution of Power Residues and Non-Residues.- An Elementary Proof of a General Theorem in Analytic Number Theory.- On the Distribution of Indices.- On a Bound for the Least nth Power Non-Residue.- On the Distribution of Fractional Parts of Values of a Function of One Variable.- On the Distribution of Fractional Parts of Values of a Function of Two Variables.- On Waring's Theorem.- A New Estimate for G (n) in Waring's Problem.- On the Upper Bound for G (n) in Waring's Problem.- New Estimates for Weyl Sums.- Representation of an Odd Number as the Sum of Three Primes.- Estimates of Certain Simple Trigonometric Sums with Prime Numbers.- Certain Problems in Analytic Number Theory.- On the Distribution of the Fractional Parts of Values of a Polynomial.- The Method of Trigonometric Sums in Number Theory.- Special Variants of the Method of Trigonometric Sums.- Ivan Matveevic Vinogradov: A Brief Outline of His Life and Works.- A Chronological List of I. M. Vinogradov's Works.