On the asymmetric divisor problem with congruence conditions

Manfred Kühleitner

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 1, page 99-116
  • ISSN: 0010-2628

Abstract

top
A certain generalized divisor function d * ( n ) is studied which counts the number of factorizations of a natural number n into integer powers with prescribed exponents under certain congruence restrictions. An Ω -estimate is established for the remainder term in the asymptotic for its Dirichlet summatory function.

How to cite

top

Kühleitner, Manfred. "On the asymmetric divisor problem with congruence conditions." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 99-116. <http://eudml.org/doc/247895>.

@article{Kühleitner1996,
abstract = {A certain generalized divisor function $d^*(n)$ is studied which counts the number of factorizations of a natural number $n$ into integer powers with prescribed exponents under certain congruence restrictions. An $\Omega $-estimate is established for the remainder term in the asymptotic for its Dirichlet summatory function.},
author = {Kühleitner, Manfred},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {multidimensional asymmetric divisor problems; -results; error term; asymptotic formula; summatory function; asymmetric divisor problem},
language = {eng},
number = {1},
pages = {99-116},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the asymmetric divisor problem with congruence conditions},
url = {http://eudml.org/doc/247895},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Kühleitner, Manfred
TI - On the asymmetric divisor problem with congruence conditions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 1
SP - 99
EP - 116
AB - A certain generalized divisor function $d^*(n)$ is studied which counts the number of factorizations of a natural number $n$ into integer powers with prescribed exponents under certain congruence restrictions. An $\Omega $-estimate is established for the remainder term in the asymptotic for its Dirichlet summatory function.
LA - eng
KW - multidimensional asymmetric divisor problems; -results; error term; asymptotic formula; summatory function; asymmetric divisor problem
UR - http://eudml.org/doc/247895
ER -

References

top
  1. Apostol T.M., Introduction to analytic number theory, New York-Heidelberg-Berlin, Springer, 1976. Zbl1154.11300MR0434929
  2. Berndt B., On the average order of a class of arithmetic functions, I, J. Number Theory 3 (1971), 184-203. (1971) MR0284409
  3. Berndt B., On the average order of a class of arithmetic functions, II, J. Number Theory 3 184-203 (1971). (1971) MR0284409
  4. Chandrasekharan K., Narasimhan R., The approximate functional equation for a class of zeta-functions, Math. Ann. 152 30-64 (1963). (1963) Zbl0116.27001MR0153643
  5. Hafner J.L., The distribution and average order of the coefficients of Dedekind ζ functions, J. Number Theory 17 183-190 (1983). (1983) Zbl0515.10042MR0716941
  6. Hafner J.L., New omega results in a weighted divisor problem, J. Number Theory 28 240-257 (1988). (1988) Zbl0635.10037MR0932373
  7. Ivić A., The Riemann zeta-function, New York, 1966. 
  8. Krätzel E., Lattice Points, Dordrecht-Boston-London, Kluwer, 1988. MR0998378
  9. Landau E., Elementary Number Theory. 2 n d ed., New York 1966, . 
  10. Nowak W.G., On the Piltz divisor problem with congruence conditions, Proc. CNTA Conference, Banff, 1988, (ed. R.A. Mollin) 455-469 (1990). Zbl0731.11052MR1106679
  11. Nowak W.G., On the Piltz divisor problem with congruence conditions II, Abh. Math. Sem. Univ. Hamburg 60 153-163 (1990). (1990) Zbl0731.11052MR1087125
  12. Nowak W.G., On the general asymmetric divisor problem, Abh. Math. Sem. Hamburg 65 (1995), to appear. (1995) Zbl0854.11048MR1359135
  13. Steinig J., On an integral connected with the average order of a class of arithmetical functions, J. Number Theory 4 463-468 (1972). (1972) Zbl0241.10028MR0306096
  14. Szegö P., Walfisz A., Über das Piltzsche Teilerproblem in algebraischen Zahlkörpern (Erste Abhandlung), Math. Z. 26 138-156 (1927). (1927) MR1544849
  15. Szegö P., Walfisz A., Über das Piltzsche Teilerproblem in algebraischen Zahlkörpern (Zweite Abhandlung), Math. Z. 26 467-486 (1927). (1927) MR1544868
  16. Titchmarsh E.C., The theory of the Riemann zeta-function, Oxford, 1951. Zbl0601.10026MR0046485

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.