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On Complex Explicit Formulae Connected with the Möbius Function of an Elliptic Curve

Published online by Cambridge University Press:  20 November 2018

Adrian Łydka
Adrian Łydka*
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland e-mail: adrianl@amu.edu.pl
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Abstract

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We study analytic properties function $m\left( z,\,E \right)$ , which is defined on the upper half-plane as an integral from the shifted $L$ -function of an elliptic curve. We show that $m\left( z,\,E \right)$ analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for $m\left( z,\,E \right)$ in the strip $\left| \Im z \right|\,<\,2\pi$ .

Keywords

11M3611G40L-functionMöbius functionexplicit formulaeelliptic curve

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014, pp. 381 - 389
Copyright
Copyright © Canadian Mathematical Society 2014

References

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