Dr Benjamin Kane (Radboud Universiteit Nijmegen)

will speak on

Some effectively computable applications of GRH

Time: 5:00PM
Date: Wed 2nd April 2008
Location: Mathematical Sciences Seminar Room [map]

Abstract: In this talk, we will discuss how under certain Generalized Riemann
Hypotheses the following questions may be answered in an effective,
explicit, and efficient manner. Firstly, we show how these
assumptions give an explicit algorithm to determine the set of
integers represented by a given ternary quadratic form of a certain
type. Next, let the ring of integers of an imaginary quadratic field
be fixed, and consider all elliptic curves with CM by this ring. We
give an algorithm to determine the image of the reduction map modulo
a given prime to supersingular elliptic curves, and in particular to
determine if it is surjective. Finally, fix a set of positive
integers S and consider the function f(x)=sum_{i=1}^{k} b_i
T_{x_i}, where T_n is the n-th triangular number. Under GRH, we
will give an explicit algorithm to determine whether f represents
every integer in S.

Please note the time.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)

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