7 papers
Mordell--Tornheim zeta function: Kronecker limit type formulas and Special values
Sumukha Sathyanarayana, N. Guru Sharan
In this paper, we establish Kronecker limit type formulas for the generalized Mordell--Tornheim zeta function as a function of the third variable, in terms of Riemann-…
Equivalence criteria for the two-term functional equations for Herglotz-Zagier functions
Sumukha Sathyanarayana, N. Guru Sharan
For any integer and non-negative integer , we define a Herglotz--Zagier (HZ) type function by an absolutely convergent series involving the Digamma function $ψ(…
On a function of Ramanujan twisted by a logarithm
Atul Dixit, Sumukha Sathyanarayana, N. Guru Sharan
A two-term functional equation for an infinite series involving the digamma function and a logarithmic factor is derived. A modular relation on page 220 of Ramanujan's Lost Noteboo…
The Mordell-Tornheim zeta function: Kronecker limit type formula, Series Evaluations and Applications
Sumukha Sathyanarayana, N. Guru Sharan
In this paper, we establish Kronecker limit type formulas for the Mordell-Tornheim zeta function as a function of the second as well as the third arguments. As an appl…
Mordell-Tornheim zeta functions and functional equations for Herglotz-Zagier type functions
Atul Dixit, Sumukha Sathyanarayana, N. Guru Sharan
The Mordell-Tornheim zeta function and the Herglotz-Zagier function are two important functions in Mathematics. By generalizing a special case of the former, namely $Θ(z, x)…
An asymptotic expansion for a twisted Lambert series associated to a cusp form and the Möbius function: level aspect
Bibekananda Maji, Sumukha Sathyanarayana, B. R. Shankar
Recently, Juyal, Maji, and Sathyanarayana have studied a Lambert series associated with a cusp form over the full modular group and the Möbius function. In this paper, we investiga…