6 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(…
Rook decomposition of the Partition function
N. Guru Sharan
The rook numbers are fairly well-studied in the literature. In this paper, we study the max-rook number of the Ferrers boards associated to integer partitions. We show its connecti…
Partitions with Durfee triangles of fixed size
N. Guru Sharan, Armin Straub
A well-studied statistic of an integer partition is the size of its Durfee square. In particular, the number of partitions of with Durfee square of fixed size has…
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)…