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

  • Alina Bucur
  • Anne-Maria Ernvall-Hytönen
  • Almasa Odžak
  • Edva Roditty-Gershon
  • Lejla Smajlović
Conference paper

DOI: 10.1007/978-3-319-17987-2_7

Volume 2 of the book series Association for Women in Mathematics Series (AWMS)
Cite this paper as:
Bucur A., Ernvall-Hytönen AM., Odžak A., Roditty-Gershon E., Smajlović L. (2015) On τ-Li Coefficients for Rankin–Selberg L-Functions. In: Bertin M., Bucur A., Feigon B., Schneps L. (eds) Women in Numbers Europe. Association for Women in Mathematics Series, vol 2. Springer, Cham

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.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Alina Bucur
    • 1
  • Anne-Maria Ernvall-Hytönen
    • 2
  • Almasa Odžak
    • 3
  • Edva Roditty-Gershon
    • 4
  • Lejla Smajlović
    • 3
  1. 1.Department of MathematicsLa JollaUSA
  2. 2.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  3. 3.Department of MathematicsUniversity of SarajevoSarajevoBosnia & Herzegovina
  4. 4.Raymond and Beverly Sackler School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael