Web Page of the Ottawa-Carleton Number Theory Seminar

Year 2010-2011

Speaker: Damien Roy, University of Ottawa
Title: A small value estimate in dimension two
Abstract: A small value estimate is a statement providing necessary conditions for the existence of a sequence of non-zero polynomials with integer coefficients taking small values at many points of an algebraic group. Such statements are desirable for applications to transcendental number theory, but only few instances of them are known at the moment. The purpose of this talk is to present a small value estimate for the product Ga x Gm of the additive group Ga by the multiplicative group Gm. We will show that if a sequence of polynomials with integer coefficients take small values at a point (xi,eta) together with its first derivatives with respect to the invariant derivation d/dx+y*d/dy, then both xi and eta are algebraic over Q. The precise statement compares favorably with constructions coming from Dirichlet's box principle.

Speaker: Abdellah Sebbar, University of Ottawa
Title: On the critical points of modular forms
Abstract: In this talk, we study the critical points of modular forms. In particular, we prove that for each modular form f for a discrete group G, its derivative f' has infinitely many non-equivalent zeros, and all, but a finite number, are simple.

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