4 papers
Distribution and Non-vanishing of special values of -series attached to Erdős functions
Siddhi Pathak
In a written correspondence with A. Livingston, Erdős conjectured that for any arithmetical function , periodic with period , taking values in when and…
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…
On a conjecture of Livingston
Siddhi Pathak
In an attempt to resolve a folklore conjecture of Erdős regarding the non-vanishing at of the -series attached to a periodic arithmetical function with period and valu…