Skip to main content
SpringerLink
Log in

On theta type functions associated with the zeros of the Selberg zeta functions

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

In this paper, we consider a kind of theta type function concerning the zeros of the Selberg zeta function. This is obtained from an application of Cartier-Voros type Selberg trace formula for non co-compact but co-finite volume discrete subgroups ofPSL(2, R).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cartier, P., Voros, A.,Une nouvelle interprétation de la formule de trace de Selberg, Grothendieck Festschrift 2, Birkhäuser, 1990, pp. 1–67.

  2. Cramér, H.,Studien über die Nullstellen der Riemannschen Zetafunktion, Math. Z.4 (1919), 104–130.

    Article  Google Scholar 

  3. Efrat, I.,Determinants of Laplacians on surfaces of finite volume, Commun. Math. Phys.119 (1988), 443–451;Erratum, ib. id.138 (1991), 607.

    Article  MATH  Google Scholar 

  4. Erdélyi, A. et al.,Table of integral transformations I, Mcgraw Hill, 1954.

  5. Fischer, J.,An approach to the Selberg trace formula via the Selberg zeta function, Lecture Note in Math., vol.1253, Springer, 1987.

  6. Hirano, M.,On Cartier-Voros type Selberg trace formula for congruence subgroups of PSL(2, R), Proc. Japan Acad.71A (1995), 144–147.

    Google Scholar 

  7. Jorgenson, J. and Lang, S.,On Cramér’s theorem for general Euler products with functional equation, Math. Ann.297 (1993), 383–416.

    Article  MATH  Google Scholar 

  8. Koyama, S.,Determinant expression of Selberg zeta functions III, Proc. A. M. S.113 (1991), 303–311.

    Article  MATH  Google Scholar 

  9. Venkov, A. B.,Spectral theory of automorphic functions, Proc. Steklov Inst. Math.153 (1982).

  10. Whittaker, E. T., Watson, G. N.,A course of modern analysis (4th. ed.), Cambridge Univ. Press, 1927.

Download references

Author information

Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, 153, Tokyo, Japan

    Miki Hirano

Authors
  1. Miki Hirano
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hirano, M. On theta type functions associated with the zeros of the Selberg zeta functions. Manuscripta Math 92, 87–105 (1997). https://doi.org/10.1007/BF02678183

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02678183

Keywords

Search

Navigation