Matyáš Lerch’s work on number theory. (English) Zbl 0874.11005

Lepka, Karel

Brno: Masaryk Univ., Fac. of Science, 78 p. (1995).

Matyáš Lerch (1860-1922) published more than 50 papers in number theory, dealing mostly with the class number of quadratic forms. This book starts with a short biography of Lerch and then brings reviews of his number-theoretical papers, taken from the Jahrbuch über die Fortschritte der Mathematik. Finally four papers of M. L. Lerch are reprinted: the first [Prager Berichte, 414-417 (1885; JFM 18.0135.01)] gives an analytical expression for the greatest common divisor of two integers, the second [Math. Ann. 60, 471-490 (1905; JFM 36.0266.03)] (not in Acta Math. as stated on p. 43) and the third [C. R. Acad. Sci. Paris 142, 35-38 (1906; JFM 37.0225.02)] deal with Fermat’s quotient \((a^{p-1}-1)/p\) and the last [Publ. Univ. Masaryk, Nr. 34, 39-44 (1923; JFM 49.0093.03)] is concerned with the distribution of quadratic residues and non residues.

Reviewer: W.Narkiewicz (Wrocław)

MSC:

11-03	History of number theory
01A55	History of mathematics in the 19th century
11A05	Multiplicative structure; Euclidean algorithm; greatest common divisors
11A15	Power residues, reciprocity
01A60	History of mathematics in the 20th century

Keywords:

greatest common divisor; Fermat quotients; quadratic residues

Citations:

JFM 18.0135.01; JFM 36.0266.03; JFM 37.0225.02; JFM 49.0093.03