Dear all,

**Talk Announcement:**

**Title:**Linear independence of numbers

**Speaker:**Sonika Dhillon (ISI, Delhi)

**When:**Thursday, Thursday Nov 23, 2023 - 4:00 PM (IST)

**Where**: Zoom: Write to the organisers for the link

**Abstract.**

In 2007, Murty and Saradha studied the linear independence of special values of digamma function $\psi(a/q)+\gamma$ over some specific numbers fields which also imply the non-vanishing of $L(1,f)$ for any rational-valued Dirichlet type function $f$. In 2009, Gun, Murty and Rath studied the non-vanishing of $L'(0,f)$ for even Dirichlet-type periodic $f$ in terms of $L(1,\hat{f})$ and established that this is related to the linear independence of logarithm of gamma values. In this direction, they made a conjecture which they call it as a variant of Rohrlich conjecture concerning the linear independence of logarithm of gamma values. In this talk, first we will discuss the linear independence of digamma values over the field of algebraic numbers. Later, we provide counterexamples

to this variant of Rohrlich conjecture.