Abstract : The Dedekind eta function is known to satisfy certain transformation formula under the action of 2 by 2 matrices with integer entries a, b, c, d with ad-bc=1. In this talk, we will begin with a transformation formula involving Dedekind sums satisfied by the Dedekind eta-function (see Apostol's ``Modular functions and Dirichlet series''). We simplify this formula and replace the expression involving Dedekind sums with polynomial expressions in terms of a,b,c and d. This formula is different from that given in H. Rademacher's book ``Topics in Analytic Number Theory'' but coincides with the formula used by G.H. Hardy and S. Ramanujan in their article on the asymptotic formula for the partition function p(n). (This is joint work with Teoh Guan Chua.)
The transformation formula for the Dedekind eta-function
16.08.2016 10:30 - 11:30
Organiser:
M. Schlosser
Location: