Sierpinski's contribution to the number theory

Andrzej Schinzel

Antiquitates Mathematicae, Tome 5 (2011), p. 227–236.

Résumé

A survey of Sierpiński's papers devoted to analytic number theory, to expansions of real numbers into series and products, to diophantine approximation and to elementary number theory.

Détail

DOI : 10.14708/am.v5i0.585

Classification : 01A50, 01A55, 01A60
Mots-clés : number theory, prime numbers, history of mathematics

Bibliographie

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[5] P. Erdos and A. Schinzel, Distribution of the values of a class of arithmetical func tions, Acta Arith. 6 (1961), 473-485, poprawiona wersja w A. Schinzel, Selecta, vol. 2 , 877-889.

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On a question of A. Schinzel concerning the sum $\sum_{n\leq x}(r(n))^2$

, in: Osterreichisch-Ungarisch-Slovakisches Kolloquium fiber Zahlenthe- orie (Marie Trost 1992), Grazer Math. Ber. 318, Karl-Franzens-Univ. Graz, Graz 1993, 63-67.

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О

знакопеременных

рядах

,

которые

могут

быть

связаны

с

двумя

алгоритмами

М

.

В

.

Остроградского

для

при

­

ближения

иррациональных

чисел

,

Успехи Мат. Наук (н.с.) 6 (1951), вып. 5 (45), 33-42.

[17] A. Schinzel, On an analytic problem considered by Sierpiński and Ramanujan, in: New Trends in Probability and Statistics, vol. 2 , Analytie and Probabilistic Methods in Number Theory, VSP Utrecht & TEV Vilnius 1992, 165-171; Selecta, vol. 2, 1217-1223.

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[20] G. Stratemeyer, Entwicklung positiver Zahlen nach Strammbruchen (Dissertation), Mitteil. math. Seminars Univ. Gieissen, Bd II, H. 20 (1932), 3-10, 25.

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Целые

точки

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круговых

конусах

,

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[23] D. Wolke, Primes with preassigned digits, Acta Arith. 119 (2005), 201- 203.