Sunday, November 19, 2023

Sonika Dhillon (ISI, Delhi) - Thursday, Thursday Nov 23, 2023 - 4:00 PM (IST)

 Dear all,

The talk this week is by Sonika Dhillon, ISI, Delhi. The announcement is as follows. 

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

Let $\psi(x)$ denote the digamma function that is the logarithmic derivative of $\Gamma$ function.
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.

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