Alladi Ramakrishnan Hall

On quotients of derivatives of Modular L functions

Rashi Lunia

IMSc

In 2011, Gun Murty and Rath studied the non-vanishing and transcendence of quotients of derivatives of $L$-functions associated to cuspidal eigenforms at the critical point. Tanabe extended their results in the setup of Hilbert modular forms and Kumar in the set-up of half-integer weight modular forms, Siegel modular forms of genus $2$ and quadratic twists of cuspidal Hecke eigenforms. In this talk, we report on a recent work where we extend these results to arbitrary points in the critical strip.
We also study the transcendental nature of special values of higher order derivatives.