Original scientific paper

https://doi.org/10.3336/gm.59.1.02

On the boundedness of Euler-Stieltjes constants for the Rankin-Selberg \(L-\)function

Medina Zubača ; Department of Mathematical and Computer Sciences, University of Sarajevo, Zmaja od Bosne 35, 71 000 Sarajevo, Bosnia and Herzegovina

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Abstract

Let \(E\) be a Galois extension of \(\mathbb{Q}\) of finite degree and let \(\pi \) and \(\pi'\) be two irreducible automorphic unitary cuspidal representations of \(GL_m(\mathbb{A}_E)\) and \(GL_{m'}(\mathbb{A}_E)\), respectively. Let \(\Lambda(s,\pi\times\widetilde{\pi}')\) be a Rankin-Selberg \(L-\)function attached to the product \(\pi\times\widetilde{\pi}'\), where \(\widetilde{\pi}'\) denotes the contragredient representation of \(\pi'\), and let its finite part (excluding Archimedean factors) be \(L(s,\pi\times\widetilde{\pi}')\).
The Euler-Stieltjes constants of the Rankin-Selberg \(L-\)function are the coefficients in the Laurent (Taylor) series expansion around \(s=1+it_0\) of the function \(L(s, \pi \times \widetilde{\pi}')\). In this paper, we derive an upper bound for these constants.

Keywords

Euler-Stieltjes constants, Rankin-Selberg \(L-\)function

Hrčak ID:

318149

URI

https://hrcak.srce.hr/318149

Publication date:

20.6.2024.

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