7 papers · 1 filter
Counting ideals in abelian number fields
Alessandro Languasco, Rashi Lunia, Pieter Moree
Already Dedekind and Weber considered the problem of counting integral ideals of norm at most in a given number field . Here we improve on the existing results in case $K/\m…
Diophantine approximation and the subspace theorem
Shivani Goel, Rashi Lunia, Anwesh Ray
Diophantine approximation explores how well irrational numbers can be approximated by rationals, with foundational results by Dirichlet, Hurwitz, and Liouville culminating in Roth'…
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…
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…
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…
Explicit upper bounds on the average of Euler-Kronecker constants of narrow ray class fields
Neelam Kandhil, Rashi Lunia, Jyothsnaa Sivaraman
For a number field , the Euler-Kronecker constant associated to is an arithmetic invariant the size and nature of which is linked to some of the deepest questions in n…