15 citations · 58 across the 22 of their papers we have counts for
23 papers
Fermat quotients and the Ankeny-Artin-Chowla conjecture
Nic Fellini, M. Ram Murty
In this article, we present streamlined proofs of results of Ankeny, Artin, and Chowla concerning the fundamental unit of the real quadratic field for primes…
From the Birch and Swinnerton-Dyer conjecture to Nagao's conjecture
Seoyoung Kim, M. Ram Murty
Let be an elliptic curve over with discriminant . For primes of good reduction, let be the number of points modulo and write . In 1…
Smooth arithmetical sums over k-free integers
Francesco Cellarosi, M. Ram Murty
We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth k-free integers.
Special values of derivatives of -series and generalized Stieltjes constants
M. Ram Murty, Siddhi Pathak
The connection between derivatives of for periodic arithmetical functions at and generalized Stieltjes constants has been noted earlier. In this paper, we utiliz…
A vanishing criterion for Dirichlet series with periodic coefficients
Tapas Chatterjee, M. Ram Murty, Siddhi Pathak
We address the question of non-vanishing of where is an algebraic-valued, periodic arithmetical function. We do this by characterizing algebraic-valued, periodic funct…
Transcendental sums related to the zeros of zeta functions
Sanoli Gun, M. Ram Murty, Purusottam Rath
While the distribution of the non-trivial zeros of the Riemann zeta function constitutes a central theme in Mathematics, nothing is known about the algebraic nature of these non-tr…