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2015 | OriginalPaper | Chapter

On τ-Li Coefficients for Rankin–Selberg L-Functions

Authors : Alina Bucur, Anne-Maria Ernvall-Hytönen, Almasa Odžak, Edva Roditty-Gershon, Lejla Smajlović

Published in: Women in Numbers Europe

Publisher: Springer International Publishing

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Abstract

The generalized τ-Li criterion for a certain zeta or L-function states that non-negativity of τ-Li coefficients associated to this function is equivalent to non-vanishing of this function in the region Re s > τ∕2. For τ ∈ [1, 2) and positive integers n, we define τ-Li coefficients \(\lambda _{n}(\pi \times \pi ',\tau )\) associated to Rankin–Selberg L-functions attached to convolutions of two cuspidal, unitary automorphic representations π and π′. We investigate their properties, including the archimedean and non-archimedean terms, and the asymptotic behavior of these terms.

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previous chapter Symmetries of Rational Functions Arising in Ecalle’s Study of Multiple Zeta Values

next chapter Galois Representations and Galois Groups Over ℚ

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Title: On τ-Li Coefficients for Rankin–Selberg L-Functions
Authors: Alina Bucur
Anne-Maria Ernvall-Hytönen
Almasa Odžak
Edva Roditty-Gershon
Lejla Smajlović
Publisher: Springer International Publishing
Book: Women in Numbers Europe
Print ISBN: 978-3-319-17986-5

Electronic ISBN: 978-3-319-17987-2

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-319-17987-2_7

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