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, Voronoĭ, 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.

Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.

Readership

Historians, graduate students, and research mathematicians interested in number theory and mathematical history.

Reviews

"(Readers) encounter a marvelous cross-section of topics from 19th and early 20th century number theory, very classical themes today, and certainly possessed of a classical beauty. ... It's a very interesting book on a number of counts."

-- MAA Reviews

"The book should be very interesting to a broad mathematical community, in particular mathematicians working in number theory as well as historians of mathematics concentrating on the development of mathematics in the second part of the 19th century."

-- EMS Newsletter

Table of Contents

• Pafnutiĭ L'vovich Chebyshev
• Chebyshev's articles on the prime numbers

• Aleksandr Nikolaevich Korkin
• The articles of Korkin and Zolotarev on the minima of positive quadratic forms

• Egor Ivanovich Zolotarev
• Zolotarev's memoirs on the theory of ideal numbers

• Andreĭ Andreevich Markov
• On binary quadratic forms of positive determinant

• Georgiĭ Fedoseevich Voronoĭ
• Voronoĭ's dissertations on algebraic numbers of the third degree
• Voronoĭ's memoir of 1903: "On a problem from the theory of asymptotic functions"
• Voronoĭ's memoirs on quadratic forms

• 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