# 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.