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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

New results on automorphic integrals and their period functions


Author: Richard A. Cavaliere
Journal: Trans. Amer. Math. Soc. 301 (1987), 401-412
MSC: Primary 11F03
MathSciNet review: 879581
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Abstract: Automorphic integrals, being generalizations of automorphic forms on discrete subgroups of $ SL(2,\,\mathbf{R})$, share properties similar to those of forms. In this article I obtain a natural boundary result for integrals which is similar to that which holds for forms. If an automorphic integral on a given group behaves like a form on a subgroup of finite index (i.e., the period functions are identically zero), then in fact the integral must be a form on the whole group. Specializing to modular integrals with integer dimension I obtain a lower bound on the number of poles of the period functions which, of necessity, lie in quadratic extensions of the rationals.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0879581-8
PII: S 0002-9947(1987)0879581-8
Article copyright: © Copyright 1987 American Mathematical Society