Acta Mathematica Hungarica
Volume/Issue:
Volume 134: Issue 1-2
A mean value theorem for the Diophantine equation axy−x−y=n
Author: Jingjing Huang 1
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  • 1 Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA, 16802-6401, U.S.A.
DOI:
https://doi.org/10.1007/s10474-011-0164-5
Page Count:
68–78
Publication Date:
01 Jan 2012
Online Publication Date:
06 Oct 2011
Article Category:
Research Article
Restricted access

We prove an asymptotic formula for the average number of solutions to the Diophantine equation axy−x−y=n in which a is fixed and n varies.

  • [1] Misiurewicz, M. 1966 Ungelöste Probleme Elem. Math. 21 90.

  • [2] Montgomery, H. L. 1971 Topics in Multiplicative Number Theory . Springer-Verlag.

  • [3] Montgomery, H. L., Vaughan, R. C. 2007 Multiplicative Number Theory I. Classical Theory Cambridge University Press.

  • [4] Titchmarsh, E. C., The Riemann Zeta-Function, 2nd ed., revised by Heath-Brown, D. R. (Oxford, 1986).

  • [5] Viola, C. 1973 On the diophantine equation and Acta Arith. 22 339–352.
Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632
Keywords:
Diophantine equation; mean value theorem; 11D45; 11D09

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