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The Selberg trace formula for modular correspondences

Published online by Cambridge University Press:  22 January 2016

Shigeki Akiyama  and
Yoshio Tanigawa
Shigeki Akiyama
Affiliation:
Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, 950-21, Japan
Yoshio Tanigawa
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan
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In Selberg [11], he introduced the trace formula and applied it to computations of traces of Hecke operators acting on the space of cusp forms of weight greater than or equal to two. But for the case of weight one, the similar method is not effective. It only gives us a certain expression of the dimension of the space of cusp forms by the residue of the Selberg type zeta function. Here the Selberg type zeta function appears in the contribution from the hyperbolic conjugacy classes when we write the trace formula with a certain kernel function ([3J, [4], [7], [8], [9], [12]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 117 , March 1990 , pp. 93 - 123
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

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