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Dirichlet series constructed from periods of automorphic forms

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Abstract

We consider certain Dirichlet series of Selberg type, constructed from periods of automorphic forms. We study analytic properties of these Dirichlet series and show that they have analytic continuation to the whole complex plane.

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References

  1. Fischer, J.: An approach to the Selberg trace formula via the Selberg zeta-function. In: Lecture Notes in Mathematics, vol. 1253. Springer, Berlin (1987)

  2. Gon, Y., Tsuzuki, M.: The resolvent trace formula for rank one Lie groups. Asian J. Math. 6, 227–252 (2002)

    MATH  MathSciNet  Google Scholar 

  3. Gon, Y.: First variation of Selberg zeta functions and variational trace formulas. J. Ramanujan Math. Soc. 18, 257–280 (2003)

    MATH  MathSciNet  Google Scholar 

  4. Hashimoto, Y., Wakayama, M.: Hierarchy of the Selberg zeta functions. Lett. Math. Phys. 73, 59–70 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Katok, S.: Closed geodesics, periods and arithmetic of modular forms. Invent. Math. 80, 469–480 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kurokawa, N., Wakayama, M.: Higher Selberg zeta functions. Commun. Math. Phys. 247, 447–466 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Lebedev, N.N.: Special Functions and Their Applications. Dover Publications, New York (1972)

    MATH  Google Scholar 

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Correspondence to Yasuro Gon.

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This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) No. 23540020 and (C) No. 26400017.

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Gon, Y. Dirichlet series constructed from periods of automorphic forms. Math. Z. 281, 747–773 (2015). https://doi.org/10.1007/s00209-015-1506-8

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  • DOI: https://doi.org/10.1007/s00209-015-1506-8

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