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Eisenstein series with non-unitary twists
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초록
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.
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.
참고문헌 (7)
- A. Deitmar, "Principles of Harmonic Analysis" (2014), Springer
- A. Deitmar, "A trace formula for non-unitary representations of a uniform lattice", Math. Z., 284(3-4), pp.1199~1210 (2016)[DOI]
- J. Dixmier, "Factorisations de fonctions et de vecteurs indefiniment differentiables", Bull. Sci. Math. (2), 102(4), pp.307~330 (1978)
- H. Iwaniec, "Spectral Methods of Automorphic Forms" (2002), American Mathematical Society
- S. Katok, "Fuchsian Groups, Chicago Lectures in Mathematics" (1992), University of Chicago Press
- W. Muller, "A Selberg trace formula for non-unitary twists", Int. Math. Res. Not. IMRN, 2011(9), pp.2068~2109 (2011)
- M. A. Shubin, "Pseudodifferential Operators and Spectral Theory" (2001), Springer-Verlag
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