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Cuspidal Modular Symbols are Transportable

Published online by Cambridge University Press:  01 February 2010

William A. Stein  and
Helena A. Verrill
William A. Stein
Affiliation:
Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA, [email protected], http://modular.fas.harvard.edu/
Helena A. Verrill
Affiliation:
Institute for Mathematics, University of Hannover, Welfengarten 1, 30167 Hannover, Germany, [email protected], http://hverrill.net

Abstract

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Modular symbols of weight 2 for a congruence subgroup Γ satisfy the identity {α,γ,(α)}={β,γ(β)} for all α,β in the extended upper half plane and γ ∊ Γ. The analogue of this identity is false for modular symbols of weight greater than 2. This paper provides a definition of transportable modular symbols, which are symbols for which an analogue of the above identity holds, and proves that every cuspidal symbol can be written as a transportable symbol. As a corollary, an algorithm is obtained for computing periods of cuspforms.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 4 , 2001 , pp. 170 - 181
Copyright
Copyright © London Mathematical Society 2001

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