International Seminar on Automorphic Forms

Cormac O’Sullivan (CUNY)): Topographs and some infinite series
The Fibonacci numbers are a familiar recursive sequence. Topographs are a kind of two dimensional version conjured up by J.H. Conway in his study of integral binary quadratic forms. These forms are ax^2 + bxy + cy^2 with integer coefficients, and have a long history in number theory. We’ll review Conway’s classification of topographs into 4 types and look at some new discoveries. Applications are to new class number formulas and a simplification of a proof of Gauss related to sums of three squares. We’ll also see how several infinite series over all the numbers in a topograph may be evaluated explicitly. This generalizes and extends results of Hurwitz and more recent authors and requires a certain Poincare series.

https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits)