Tohoku Mathematical Journal

Regularized periods of automorphic forms on $GL(2)$

Shingo Sugiyama

Full-text: Open access

Abstract

In this paper, we study regularized periods of cusp forms and Eisenstein series on $GL(2)$ introduced by Masao Tsuzuki.

Article information

Source
Tohoku Math. J. (2), Volume 65, Number 3 (2013), 373-409.

Dates
First available in Project Euclid: 12 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1378991022

Digital Object Identifier
doi:10.2748/tmj/1378991022

Mathematical Reviews number (MathSciNet)
MR3102541

Zentralblatt MATH identifier
1328.11054

Subjects
Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields

Keywords
Automorphic representations period integrals

Citation

Sugiyama, Shingo. Regularized periods of automorphic forms on $GL(2)$. Tohoku Math. J. (2) 65 (2013), no. 3, 373--409. doi:10.2748/tmj/1378991022. https://projecteuclid.org/euclid.tmj/1378991022


Export citation

References

  • D. Bump, Automorphic forms and representations, Cambridge Stud. Adv. Math. 55, Cambridge University Press, Cambridge, 1997.
  • R. Godement, Notes on Jacquet-Langlands' theory, The Institute for Advanced Study, 1970.
  • D. Goldfeld, Automorphic forms and $L$-functions for the group $GL(n; R)$, Cambridge Stud. Adv. Math. 99. Cambridge University Press, Cambridge, 2006.
  • H. Jacquet and R. P. Langlands, Automorphic forms on $GL(2)$, Lecture Notes in Math. 114, Springer-Verlag, Berlin-New York, 1970.
  • D. Ramakrishnan and R. J. Valenza, Fourier analysis on number fields, Grad. Texts in Math. 186, Springer-Verlag, New York, 1999.
  • B. Roberts and R. Schmidt, Local new forms for $GSp(4)$, Lecture Notes in Math. 1918, Springer-Verlag, Berlin-New York, 2007.
  • R. Schmidt, Some remarks on local newforms for $GL(2)$, J. Ramanujan Math. Soc. 17 (2002), 115–147.
  • H. Shimizu, Automorphic functions (in Japanese), Iwanamishoten, 1978.
  • M. Tsuzuki, Spectral means of central values of automorphic $L$-functions for $GL(2)$, to appear in Mem. Amer. Math. Soc.
  • J.-L. Waldspurger, Sur les valeurs de certaines fonctions $L$ automorphes en leur centre de symetrie, Compositio Math. 54 (1985), 173–242.
  • A. Yukie, Shintani zeta functions, London Math. Soc. Lecture Note Ser. 183, Cambridge University Press, Cambridge, 1993.