Yegor Ivanovich Zolotaryov

Yegor Solotaryov

Yegor Ivanovich Solotarev ( Russian Егор Иванович Золотарёв , also Solotareff, Zolotareff, in English sometimes Egor Zolotarev; born March 31, 1847 in Saint Petersburg ; † July 19, 1878 ibid) was a Russian mathematician who dealt specifically with number theory.

life and work

The son of the businessman Ivan Wassiljewitsch Solotarjow attended the fifth (mathematical and scientific-oriented) grammar school in his hometown of Saint Petersburg from 1857-1863, which he graduated with honors, before he was immediately admitted to the university there and officially started studying in 1864 could begin with Pafnuti Chebyshev and Alexander Korkin . In 1867 he published a work on the integration of gyroscopic equations, for which he was awarded the title of candidate of the sciences . In 1868 his "Thesis pro venia legendi" ( About a minimal problem ) followed, making him a private lecturer at St. Petersburg University . From then on he read mainly about analysis and elliptic functions. In 1869 the Magister dissertation followed (it corresponds more to the German doctorate) on the solutions to a cubic equation of the form x³ + Ay³ + A²z³ - 3Axyz = 1 in whole numbers. In 1872 he made his first trip abroad to Berlin , where he heard from Karl Weierstrass and Ernst Eduard Kummer , to Heidelberg to Leo Koenigsberger and to Paris to Charles Hermite .

In 1874 he became a professor at the University of St. Petersburg and defended his doctoral thesis ( theory of complex numbers with application to integral calculus ), in which he solved a problem his teacher Chebyshev had tried in vain to solve. His work consisted in finding elliptic integrals of the form:

${\displaystyle \int {\frac {x+A}{\sqrt {x^{4}+ax^{3}+bx^{2}+cx+d}}}\,\mathrm {d} x}$

to be expressed by logarithmic functions. In 1876 he became an associate professor and, at the same time, an associate member of the Academy of Sciences, succeeding Somov . His career ended abruptly when he was run over by a train on the way to his dacha in Tsarskoye Selo Station in July 1878 and died of blood poisoning shortly afterwards.

Solotarev is best known today for his contributions to the theory of quadratic forms, where he collaborated with Korkin, and to algebraic number theory, with the first approaches of a valuation theory. In 1872 he presented an inventive proof of the quadratic reciprocity law , which is based on the representation of the Legendre symbol as the sign of a special permutation ( Lemma von Zolotareff ). Following on from Chebyshev, he also dealt with approximation theory and elliptic integrals.

With Korkin he determined the closest packing of spheres on the grid in 4 and 5 dimensions.

literature

• Bashmakova in Dictionary of Scientific Biography
• J. Todd The legacy of EIZolotarev , Mathematical Intelligencer 1988, No. 2, p. 50
• Ozhigova Zolotarev , Nauka, Moscow 1966 (Russian)
• Kuzmin Life and Work of Zolotarev , Uspekhi Math.Nauka, 1947 (Russian)
• Opolka, Scharlau From Hermite to Minkowski , Springer 1980
• K.-G. Steffens The History of Approximation Theory: From Euler to Bernstein , Birkhäuser, Boston 2006

Web links

• John J. O'Connor, Edmund F. Robertson :  Yegor Iwanowitsch Solotarjow. In: MacTutor History of Mathematics archive .
• Zolotareff Sur la methode de l integration de M. Tschebychef , Mathematische Annalen 1872, French
• Korkine, G.Zolotareff Sur les formes quadratiques positives quaternaires , Mathematische Annalen 1872
• Korkine, Zolotareff Sur les formes quadratiques , Mathematische Annalen 1873
• Korkine, Zolotareff Sur les formes quadratiques positives , Mathematische Annalen 1877

Sources and footnotes

1. ↑ The Russian dissertation is more like a German habilitation
2. ↑ Eric Weis stone HyperSphere packings, tungsten Mathworld
3. ↑ Korkin, Zolotareff, Sur les formes quadratiques positives. "Math. Ann., Volume 11, 1877, pp. 242-292