### Yegor Ivanovich Zolotarev

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

Yegor Ivanovich Zolotarev (1847-1879) was one of the most remarkable of
Russian mathematicians. He completed the degree program at St Petersburg
University. He was made privat docent for his essay *On a question of least quantities* and received a Master's degree in pure mathematics for
the essay *On an indeterminate equation of degree three*.

In 1872 Zolotarev gave a proof based on the theory of elliptic functions, of
Chebyshev's method, solving the problem of the integrability of certain
algebraic differentials in finite form. In collaboration with Professor
Korkin, Zolotarev undertook to find the exact limit for the minimum of a
positive definite quadratic form. Their results appeared in three memoirs
published in the journal Mathematische Annalen **V** 1872, **VI** 1873, **XI** 1877. This solved a difficult of problem - prior to the appearance of their memoirs, only the simplest cases were known, relating to binary and ternary forms. In their memoirs they solve the problem for forms in four and five variables.

In the period 1871-1877 Zolotarev generalized the theory of so-called ideal numbers, determined by roots of unity; he extended it to complex numbers determined by the roots of an arbitrary polynomial with integer coefficients. Zolotarev then applied his theory to a question of the integral calculus representing a generalization of the above-mentioned method of Chebyshev. These results were expounded in his doctoral thesis *The theory of integral complex numbers with an application to the integral calculus* (SPB. 1874).

After obtaining his doctorate Zolotarev was appointed Extraordinary Professor and in 1877 was made an associate of the St Petersburg Academy of Sciences. Zolotarev published further results of his investigations in complex number theory in the memoir *On the theory of complex numbers*, in the Journal de Mathématiques Pures et Appliquées in 1880. He had many new works planned, but his unexpected death ended his brilliant career. Apart from the above-mentioned articles, Zolotarev published several other memoirs in the Bulletin of the St Petersburg Academy of Sciences
and other mathematical journals.
Back to some biographies of past contributors to number theory

Last updated 18th June 2003