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On the Trace of Hecke Operators for Certain Modular Groups

Published online by Cambridge University Press:  22 January 2016

Masatoshi Yamauchi
Masatoshi Yamauchi*
Affiliation:
Mathematical Institute, Nagoya University
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The trace of Hecke operators with respect to a unit group of an order in a quaternion algebra has been given in Eichler [1], [2] in the case when the order is of square-free level. The purpose of this note is to study the order of type (q1, q2, q3) (see text 1.1), in the case, of cube-free level, and to give a formula for the trace of Hecke operators in the case q3 = 2.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 43 , September 1971 , pp. 137 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Eichler, M., Lectures on Modular correspondence, Lecture note, Tata Insitute of Fundamental Research Bombay 1955/56.Google Scholar
[2] Eichler, M., Zur Zahlentheolie der Quaternionen Algebren, Journ. reine angew. Math. 195 (1956), 127–151.Google Scholar
[3] Eichler, M., Quadratische Formen und Modulfunktionen, Acta Arith., 4 (1958), 217–239.Google Scholar
[4] Shimizu, H., On traces of Hecke operators, J. Fac. Scil Univ. Tokyo 10 (1963), 1–19.Google Scholar
[5] Shimizu, H., On zeta functions of quaternion algebras, Ann. of Math., 81 (1965), 166–193.Google Scholar
[6] Shimura, G., Algebraic number fields and symplecitc discontinuous groups, Ann. of Math., 86 (1967), 503–592.Google Scholar