Rényi's formula with remainder term on arithmetical semigroups

Štefan Porubský

Mathematica Slovaca (1990)

  • Volume: 40, Issue: 1, page 37-52
  • ISSN: 0139-9918

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Porubský, Štefan. "Rényi's formula with remainder term on arithmetical semigroups." Mathematica Slovaca 40.1 (1990): 37-52. <http://eudml.org/doc/34297>.

@article{Porubský1990,
author = {Porubský, Štefan},
journal = {Mathematica Slovaca},
keywords = {generalized primes; arithmetical function; asymptotic density; arithmetical semigroup; Axiom A; analogue of Rényi’s formula},
language = {eng},
number = {1},
pages = {37-52},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Rényi's formula with remainder term on arithmetical semigroups},
url = {http://eudml.org/doc/34297},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Porubský, Štefan
TI - Rényi's formula with remainder term on arithmetical semigroups
JO - Mathematica Slovaca
PY - 1990
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 40
IS - 1
SP - 37
EP - 52
LA - eng
KW - generalized primes; arithmetical function; asymptotic density; arithmetical semigroup; Axiom A; analogue of Rényi’s formula
UR - http://eudml.org/doc/34297
ER -

References

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  1. COHEN E., Arithmetical notes VIII, An asymptotic formula of Rényi, Proc. Amer. Math. Soc. 13, 1962, 536-539. (1962) Zbl0117.27704MR0138606
  2. DELANGE H., Sur un théorème de Rényi, Acta Arithm. 11, 1965, 241-252. (1965) Zbl0131.04504MR0201398
  3. DELANGE H., Sur un théorème de Rényi II, Acta Arithm. 13, 1968, 339-362. (1968) Zbl0155.09101MR0228457
  4. DELANGE H., Sur un théorème de Rényi III, Acta Arithm. 23, 1973, 153-182. (1973) Zbl0234.10045MR0330075
  5. KÁTAI I., Egy megjegyzés H. Delange "Sur un théorème de Rényi" címü dolgozatához, MTA III. Osztály Közleményei 16, 1966, 269-273. (1966) MR0237444
  6. KNOPFMACHER J., Abstract Analytic Number Theory, North-Holland/American Elsevier, Amsterdam-New York 1975. (1975) Zbl0322.10001MR0419383
  7. KNOPFMACHER J., Arithmetic properties of finite rings and algebras, and analytic number theory, II: Categories and relative analytic number theory, J. reine angew. Math. 254, 1972, 74-99. (1972) Zbl0246.10033MR0364132
  8. LANDAU E., Handbuch der Lehre von der Verteilung der Primzahlen, zv. II. XLIV, § 162. Zbl0051.28007
  9. LANDAU E., Neuer Beweis der Gleichung n = 1 μ ( k ) k - 1 = 0 , Inauguraldissertation, Berlin 1899. 
  10. LANDAU E., Über die Äquivalenz zweier Hauptsätze der analytischen Zahlentheorie, Sitzungber. Akad. Wien, 120, Abt. 2a, 1911, 973-988. (1911) Zbl42.0222.02
  11. PORUBSKÝ Š., On the density of certain sets in arithmetical semigroups, Czechoslovak Math. J. 29, 1979, 148-152. (1979) Zbl0439.10033MR0518150
  12. RÉNYI A., On the density of certain sequences of integers, Publications de l'Institut Mathématiques de ľAcadémie Serbe des Sciences 8, 1955, 157-162. (1955) Zbl0066.03203MR0076787
  13. SCHWARZ W., Eine Bemerkung zu einer asymptotischen formel von Herrn Rényi, Arch. Math. (Basel) 21, 1970, 157-166. (1970) Zbl0197.32301MR0272730
  14. ZHANG W., A generalization of Halász' theorem to Beurling's generalized integers and its applications, Illinois J. Math. 31, 1987, 645-664. (1987) MR0909789

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