### Aleksander Nikolaevich Korkin

###### (Translation kindly provided by Bob Burns)

Aleksander Nikolaevich Korkin (1837-1908) completed the program of the Faculty of Mathematics and Physics of St. Petersburg University. He obtained his Master's degree with the dissertation *Definition of arbitrary functions in terms of the integrals of linear partial differential equations*, and his doctor's degree with the dissertation *On joint (or total or simultaneous) partial differential equations and certain questions of mechanics*. He was professor at St. Petersburg University; he gave courses in differential and integral calculus at the Nikolaevskii Naval Academy.

The scientific work of Korkin mostly concerns the solution of partial differential equations and the theory of numbers.
His master's and doctoral dissertations are devoted to the first of these
areas, as are his articles *Sur le théoreme de Poisson et son reciproque*, Bulletin de l'Acad. de St. Petersb., **XVI** 1871, *On partial differential equations of the second order* (Appendix to the university minutes, 1878) and others.

In number theory, Korkin's work is concentrated on the theory of quadratic forms. The fundamental question concerning the so-called exact limit of the minimum of definite quadratic forms, easily answered for binary forms, presented difficulties in the case of ternary forms and even greater ones in the case of forms in four and more variables. From 1871 to 1877 Korkin, in collaboration with E.I. Zolotarev, undertook a series of attempts on this problem, and they were able to solve it for forms in four and five variables. These results, of capital importance in the theory of definite quadratic forms, are expounded in articles published in Mathematische Annalen **V**,**VI** and **XI**.

A detailed list of Korkin's works has been compiled by K.A. Posse, Journal of the Ministry for the People's Enlightenment, November 1908.
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Last updated 18th June 2003