Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

EISENSTEIN SERIES WITH NON-UNITARY TWISTS

  • Received : 2017.01.09
  • Accepted : 2018.01.12
  • Published : 2018.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp forms and that Eisenstein series admit a meromorphic continuation.

Keywords

References

  1. A. Deitmar and S. Echterhoff, Principles of Harmonic Analysis, second edition, Universitext, Springer, Cham, 2014.
  2. A. Deitmar and F. Monheim, A trace formula for non-unitary representations of a uniform lattice, Math. Z. 284 (2016), no. 3-4, 1199-1210. https://doi.org/10.1007/s00209-016-1695-9
  3. J. Dixmier and P. Malliavin, Factorisations de fonctions et de vecteurs indefiniment differentiables, Bull. Sci. Math. (2) 102 (1978), no. 4, 307-330.
  4. H. Iwaniec, Spectral Methods of Automorphic Forms, second edition, Graduate Studies in Mathematics, 53, American Mathematical Society, Providence, RI, 2002.
  5. S. Katok, Fuchsian Groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1992.
  6. W. Muller, A Selberg trace formula for non-unitary twists, Int. Math. Res. Not. IMRN 2011, no. 9, 2068-2109.
  7. M. A. Shubin, Pseudodifferential Operators and Spectral Theory, translated from the 1978 Russian original by Stig I. Andersson, second edition, Springer-Verlag, Berlin, 2001.