The Taylor expansion of the Jacobi theta function at x=1

Abstract. Modular forms are traditionally studied in terms of their Fourier coefficients, but an interesting point of view that has received much less attention historically consists of studying their local behavior around a point. An example of this, which will be the subject of the talk, is to look at the Taylor expansion of the Jacobi theta function at x=1. This gives rise to an interesting sequence of integers, which seems not to have been previously studied. I will discuss work in progress in which I am studying the interesting arithmetic and combinatorial properties of this sequence.