Comparing the number of abelian groups and of semisimple rings of a given order

Manfred Kühleitner

Mathematica Slovaca (1995)

  • Volume: 45, Issue: 5, page 509-518
  • ISSN: 0139-9918

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Kühleitner, Manfred. "Comparing the number of abelian groups and of semisimple rings of a given order." Mathematica Slovaca 45.5 (1995): 509-518. <http://eudml.org/doc/31901>.

@article{Kühleitner1995,
author = {Kühleitner, Manfred},
journal = {Mathematica Slovaca},
keywords = {number of Abelian groups of a given order; number of semisimple rings of a given order; Dirichlet summatory function; arithmetic functions; asymptotic expansion},
language = {eng},
number = {5},
pages = {509-518},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Comparing the number of abelian groups and of semisimple rings of a given order},
url = {http://eudml.org/doc/31901},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Kühleitner, Manfred
TI - Comparing the number of abelian groups and of semisimple rings of a given order
JO - Mathematica Slovaca
PY - 1995
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 45
IS - 5
SP - 509
EP - 518
LA - eng
KW - number of Abelian groups of a given order; number of semisimple rings of a given order; Dirichlet summatory function; arithmetic functions; asymptotic expansion
UR - http://eudml.org/doc/31901
ER -

References

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  1. ERDÖS P., SZEKERES G., Über die Anzahl der Abelschen Gruppen gegebener Ordnung und über ein verwandtes zahlentheoretisches Problem, Acta Sei. Math. (Szeged) VII (1934), 95-102. (1934) Zbl0010.29402
  2. IVIĆ A., The Riemann Zeta-Function, J. Wiley 8z Sons, New York-Chichester-Brisbane-Toronto-Singapore, 1985. (1985) Zbl0583.10021MR0792089
  3. De KONINCK J. M., IVIĆ A., Topics in Arithmetical Functions, North Holland Publ. Co., Amsterdam-New York-Oxford, 1980. (1980) Zbl0442.10032MR0589545
  4. HONG-QUAN LIU, On the number of abelian groups of a given order, Acta Arith. LIX (1991), 261-277. (1991) MR1133246
  5. KRÄTZEL E., Lattice Points, Kluwer Acad. Publ., Dordrecht-Boston-London, 1988. (1988) Zbl0675.10031MR0998378
  6. MITSUI T., On the prime ideal theorem, J. Math. Soc. Japan 20 (1968), 233-247. (1968) Zbl0172.06102MR0223314
  7. NORTHCOTT D. G., Lessons on Rings, Modules and Multiplicities, Cambridge University Press, London, 1968. (1968) Zbl0159.33001MR0231816
  8. NOWAK W. G., On the average number of finite abelian groups of a given order, Ann. Sei. Math. Quebec 15 (1991), 193-202. (1991) Zbl0749.11043MR1151477
  9. NOWAK W. G., Sums of reciprocals of general divisor functions and the Selberg divisor problem, Abh. Math. Sem. Univ. Hamburg 61 (1991), 163-173. (1991) Zbl0739.11037MR1138281
  10. PRACHAR K., Primzahlverteilung, Springer, Berlin-Heidelberg-New York, 1957. (1957) Zbl0080.25901MR0087685
  11. RIEGER G. J., Zum Teilerproblem von Atle Selberg, Math. Nachr. 30 (1965), 181-192. (1965) MR0190105
  12. SELBERG A., Note on a paper by L. G. Sathe, J. Indian Math. Soc. 18 (1954), 83-87. (1954) Zbl0057.28502MR0067143
  13. WALFISZ A., Weylsche Exponentialsummen in der neueren Zahlentheorie, Dt. Verl. d. Wiss., Berlin, 1963. (1963) Zbl0146.06003MR0220685

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