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Chris Marks University of Alberta

Chris Marks
University of Alberta
The Bounded
Denominator Conjecture
for Vector-Valued
Modular Forms
Friday, November 26, 2010
3:30 p.m.
Mathematics and Statistics Lounge, CW 307.20
Abstract:A well-known consequence of the theory of Hecke operators is that
modular forms for congruence subgroups of the modular group PSL2(Z) have
"bounded denominators", e.g. if f is a modular form for a congruence subgroup
whose Fourier coefficients are rational numbers, then there is some large integer
M such that the Fourier coefficients of Mf are all rational integers. Atkin and
Swinnerton-Dyer were the first to observe (in the early 1970s) that this prop-
erty does not necessarily hold for noncongruence modular forms, and it has since
been conjectured that this property of having bounded denominators is in fact
equivalent to being a congruence modular form. Since the original paper of ASD
much work has been done in this area, but few techniques have emerged which


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics