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

Canadian mathematical bulletin

Adrian Łydka¹ 

[1] Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, POLAND

关键词: L-function;    Möbius function;    explicit formulae;    elliptic curve;   

DOI  :  10.4153/CMB-2013-021-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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

【 授权许可】

Unknown