Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Shintani functions on $GL(2,{\mathbf{C}})$

Author: Miki Hirano
Journal: Trans. Amer. Math. Soc. 353 (2001), 1535-1550
MSC (1991): Primary 11F70
Published electronically: November 29, 2000
MathSciNet review: 1806729
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In this paper, in analogy to the real case, we give a formulation of the Shintani functions on $GL(2,\mathbf{C})$, which have been studied by Murase and Sugano within the theory of automorphic $L$-functions. Also, we obtain the multiplicity one theorem for these functions and an explicit formula in a special case.

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Additional Information

Miki Hirano
Affiliation: Department of Mathematical Sciences, Faculty of Science, Ehime University, Ehime, 790-8577, Japan

Received by editor(s): November 23, 1999
Received by editor(s) in revised form: April 13, 2000
Published electronically: November 29, 2000
Additional Notes: This work was partially supported by JSPS Research Fellowships for Young Scientists
Article copyright: © Copyright 2000 American Mathematical Society