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

DOI:
https://doi.org/10.1090/S0002-9947-1987-0879581-8

MathSciNet review:
879581

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Abstract: Automorphic integrals, being generalizations of automorphic forms on discrete subgroups of , 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:
https://doi.org/10.1090/S0002-9947-1987-0879581-8

Article copyright:
© Copyright 1987
American Mathematical Society