International Seminar on Automorphic Forms

Zhiyuan Li (SCMS, Fudan University)

The Shintani–Faddeev modular cocycle: Stark units from q-Pochhammer ratios

We give a new interpretation of Stark units associated to real quadratic fields as special “real multiplication values” of a modular cocycle described by complex meromorphic continuation of a simple infinite product. The cocycle encodes the modular transformations of the infinite q-Pochhammer symbol and is related to the Shintani–Barnes double sine funciton and the Faddeev quantum dilogarithm. As a corollary, we describe some intriguing features of the asymptotic behavior of the infinite q-Pochhammer symbol as the modular parameter approaches a real quadratic number.

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

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