For over two centuries, the work of the St. Petersburg mathematicians in number theory has constituted a glorious contribution to mathematics. The Russian book, ""The St. Petersburg School of Number Theory"", is about the life and work of prominent members of this school, such as Chebyshev, Korkin, Zolotarev, Markov, Voronoi, and Vinogradov. These mathematicians are indeed a very distinguished group. Their work in number theory is of the highest quality and continues to have lasting significance.This English translation acquaints the reader with the most important works of these six eminent members of the St. Petersburg school. A short biography is given for each of them, followed by an exposition of some of his most significant contributions. Each contribution features the author's original terminology and notation and is followed by commentary. Certain works receive relatively complete expositions, while others are dealt with more briefly. With a Foreword written for the English edition, this volume will appeal to a broad mathematical audience, including mathematical historians. It is particularly suitable for graduate students and researchers interested in number theory.
Pafnutii L'vovich Chebyshev (1821-1894): Pafnutii L'vovich Chebyshev Chebyshev's articles on the prime numbers Aleksandr Nikolaevich Korkin (1837-1908): Aleksandr Nikolaevich Korkin The articles of Korkin and Zolotarev on the minima of positive quadratic forms Egor Ivanovich Zolotarev (1847-1878): Egor Ivanovich Zolotarev Zolotarev's memoirs on the theory of ideal numbers Andrei Andreevich Markov (1856-1922): Andrei Andreevich Markov On binary quadratic forms of positive determinant Georgii Fedoseevich Voronoi (1868-1908): Georgii Fedoseevich Voronoi Voronoi's dissertations on algebraic numbers of the third degree Voronoi's memoir of 1903: "On a problem from the theory of asymptotic functions" Voronoi's memoirs on quadratic forms Ivan Matveevich Vinogradov (1891-1983): Ivan Matveevich Vinogradov Works of Vinogradov from the first period of his mathematical activity Waring's problem The Goldbach problem Estimation of Weyl sums and the problem of the fractional parts of a polynomial Bibliography.