The average number of solutions of the Diophantine equation U²+V²=W³ and related arithmetic functions

Authors: Manfred Kühleitner¹; Werner Georg Nowak²

Source: Acta Mathematica Hungarica, Volume 104, Number 3, 2004 , pp. 225-240(16)

Publisher: Springer

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Abstract:

For the number of integer solutions of the title equation, with W

;x (x a large parameter), an asymptotics of the form Ax log x + Bx + O(x^1/2 (log x)³ (loglog x)²) is established. This is achieved in a general setting which furnishes applications to some other natural arithmetic functions.

Keywords: Diophantine equations; arithmetic functions; zeta-functions

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:AMHU.0000036284.91580.3e

Affiliations: 1: Institut für Mathematik, Universität f udblac r Bodenkultur Peter Jordan-Straße 82, A-1190 Wien, Austria, Email: kleitner@edv1.boku.ac.at r Bodenkultur Peter Jordan-Straße 82, A-1190 Wien, Austria, Email: kleitner@edv1.boku.ac.at "> 2: Institut für Mathematik, Universität f udblac r Bodenkultur Peter Jordan-Straße 82, A-1190 Wien, Austria, Email: nowak@mail.boku.ac.atr Bodenkultur Peter Jordan-Straße 82, A-1190 Wien, Austria, Email: nowak@mail.boku.ac.at">