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

  • Alina Bucur
  • Anne-Maria Ernvall-Hytönen
  • Almasa Odžak
  • Edva Roditty-Gershon
  • Lejla Smajlović
Part of the Association for Women in Mathematics Series book series (AWMS, volume 2)

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.

Keywords

Riemann Zeta Function Riemann Hypothesis Automorphic Representation Arithmetic Formula Critical Strip 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors of the paper would like to thank the organizers of the WINE conference. The conference was funded by CIRM, Microsoft research, Number theory foundation, NSF and Clay Mathematics Institute. Their support is gratefully acknowledged. The research of A.-M. E.-H. was supported by the Academy of Finland, grant no. 138337. The research of A.B. was supported by Simons Foundation Award #244988.

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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

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