Glasnik Matematicki, Vol. 51, No. 1 (2016), 23-44.

EULER-STIELTJES CONSTANTS FOR THE RANKIN-SELBERG L-FUNCTION AND WEIGHTED SELBERG ORTHOGONALITY

Almasa Odžak and Lejla Smajlović

Department of Mathematics, University of Sarajevo, Zmaja od Bosne 35, 71 000 Sarajevo, Bosnia and Herzegovina
e-mail: almasa@pmf.unsa.ba
e-mail: lejlas@pmf.unsa.ba

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.

2010 Mathematics Subject Classification.   11M26, 11S40.

Key words and phrases.   Euler-Stieltjes constants, Rankin-Selberg L-function, weighted Selberg orthogonality.

Full text (PDF) (free access)

DOI: 10.3336/gm.51.1.03

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