**History of Mathematics**

Volume: 26;
2005;
278 pp;
Hardcover

MSC: Primary 01; 11;

Print ISBN: 978-0-8218-3457-2

Product Code: HMATH/26

List Price: $74.00

AMS Member Price: $59.20

MAA Member Price: $66.60

**Electronic ISBN: 978-1-4704-3894-4
Product Code: HMATH/26.E**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

#### Supplemental Materials

# The St. Petersburg School of Number Theory

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*B. N. Delone*

A co-publication of the AMS and the London Mathematical Society

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, Vorono&ibreve;, 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.

#### Readership

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

#### Reviews & Endorsements

(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

# Table of Contents

## The St. Petersburg School of Number Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Foreword to the English edition vii8
- Preface xv16
- Pafnutiĭ L’vovich Chebyshev (1821–1894) 118
- Pafnutiĭ L’vovich Chebyshev 320
- Chebyshev’s articles on the prime numbers 724
- Aleksandr Nikolaevich Korkin (1837–1908) 2542
- Aleksandr Nikolaevich Korkin 2744
- The articles of Korkin and Zolotarev on the minima of positive quadratic forms 3148
- Egor Ivanovich Zolotarev (1847–1878) 6178
- Egor Ivanovich Zolotarev 6380
- Zolotarev’s memoirs on the theory of ideal numbers 6784
- Andreĭ Andreevich Markov (1856–1922) 91108
- Andreĭ Andreevich Markov 93110
- On binary quadratic forms of positive determinant 95112
- Georgiĭ Fedoseevich Voronoĭ (1868–1908) 129146
- Georgiĭ Fedoseevich Voronoĭ 131148
- Voronoĭ’s dissertations on algebraic numbers of the third degree 135152
- Voronoĭ’s memoir of 1903: “On a problem from the theory of asymptotic functions” 165182
- Voronoĭ’s memoirs on quadratic forms 169186
- Ivan Matveevich Vinogradov (1891–1983) 209226
- Ivan Matveevich Vinogradov 211228
- Works of Vinogradov from the first period of his mathematical activity 213230
- Waring’s problem 225242
- The Goldbach problem 243260
- Estimation of Weyl sums and the problem of the fractional parts of a polynomial 263280
- Bibliography 273290
- Back Cover Back Cover1297