Original scientific paper

https://doi.org/10.3336/gm.51.1.03

Euler-Stieltjes constants for the Rankin-Selberg L-function and weighted Selberg orthogonality

Almasa Odžak ; Department of Mathematics, University of Sarajevo, Zmaja od Bosne 35, 71 000 Sarajevo, Bosnia and Herzegovina
Lejla Smajlović ; Department of Mathematics, University of Sarajevo, Zmaja od Bosne 35, 71 000 Sarajevo, Bosnia and Herzegovina

Abstract

Let E be Galois extension of Q of finite degree and let π and π' be two irreducible automorphic unitary cuspidal representations of GLm(EA) and GLm'(EA), respectively. We prove an asymptotic formula for computation of coefficients γπ,π'(k) in the Laurent (Taylor) series expansion around s=1 of the logarithmic derivative of the Rankin-Selberg L-function L(s, π × π') under assumption that at least one of representations π, π' is self-contragredient and show that coefficients γπ,π'(k) are related to weighted Selberg orthogonality. We also replace the assumption that at least one of representations π and π' is self-contragredient by a weaker one.

Keywords

Euler-Stieltjes constants; Rankin-Selberg L-function; weighted Selberg orthogonality

Hrčak ID:

160101

URI

https://hrcak.srce.hr/160101

Publication date:

15.6.2016.

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