×

Transportable modular symbols and the intersection pairing. (English) Zbl 1057.11030

Fieker, Claus (ed.) et al., Algorithmic number theory. 5th international symposium, ANTS-V, Sydney, Australia, July 7–12, 2002. Proceedings. Berlin: Springer (ISBN 3-540-43863-7). Lect. Notes Comput. Sci. 2369, 219-233 (2002).
Summary: Transportable modular symbols were originally introduced in order to compute periods of modular forms [W. A. Stein and H. A. Verrill, LMS J. Comput. Math. 4, 170–181 (2001; Zbl 1049.11054)]. Here we use them to give an algorithm to compute the intersection pairing for modular symbols of weight \(k\geq 2\). This generalizes the algorithm given by L. Merel [Manuscr. Math. 80, No. 3, 283–289 (1993; Zbl 0812.14013)] for computing the intersection pairing for modular symbols of weight 2. We also define a certain subspace of the space of transportable modular symbols, and give numerical evidence to support a conjecture that this space should replace the usual space of cuspidal modular symbols.
For the entire collection see [Zbl 0992.00024].

MSC:

11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
PDFBibTeX XMLCite
Full Text: Link