On Complex Explicit Formulae Connected with the Möbius Function of an Elliptic Curve
Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 381-389
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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 $\left| \Im z \right|\,<\,2\pi$ .
Mots-clés :
11M36, 11G40, L-function, Möbius function, explicit formulae, elliptic curve
Łydka, Adrian. On Complex Explicit Formulae Connected with the Möbius Function of an Elliptic Curve. Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 381-389. doi: 10.4153/CMB-2013-021-3
@article{10_4153_CMB_2013_021_3,
author = {{\L}ydka, Adrian},
title = {On {Complex} {Explicit} {Formulae} {Connected} with the {M\"obius} {Function} of an {Elliptic} {Curve}},
journal = {Canadian mathematical bulletin},
pages = {381--389},
year = {2014},
volume = {57},
number = {2},
doi = {10.4153/CMB-2013-021-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-021-3/}
}
TY - JOUR AU - Łydka, Adrian TI - On Complex Explicit Formulae Connected with the Möbius Function of an Elliptic Curve JO - Canadian mathematical bulletin PY - 2014 SP - 381 EP - 389 VL - 57 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-021-3/ DO - 10.4153/CMB-2013-021-3 ID - 10_4153_CMB_2013_021_3 ER -
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