3 papers
math.NT2024
On extreme values of quadratic twists of Dirichlet-type -functions
Sanoli Gun, Rashi Lunia
In a recent work arXiv:2004.14450, it has been shown that -functions associated with arbitrary non-zero cusp forms take large values at the central critical point. The goal of t…
math.NT2024
Extreme values of -functions of newforms
Sanoli Gun, Rashi Lunia
In 2008, Soundararajan showed that there exists a normalized Hecke eigenform of weight and level one such that $$ L(1/2, f ) ~\geq~ \exp\Bigg( (1 + o(1)) \sqrt{\frac{2\log…
math.NT2024
On quotients of derivatives of -functions inside the critical strip
Rashi Lunia
In 2011, Gun, Murty and Rath studied non-vanishing and transcendental nature of special values of a varying class of -functions and their derivatives. This led to a number of wo…