Mahipal Gurram

collaborators

5 papers

math.NT2025

Explicit Lower Bounds for Dirichlet Series of Higher Power Representation Functions

Mahipal Gurram

We investigate Dirichlet-type series generated by representation functions that count the number of ways an integer can be expressed as a sum of 'k' signed higher even powers. By c…

math.GM2025

Bailey-Zeta Limits: A $q$ -Series Bridge to Dirichlet $L$ -Functions and the Riemann Zeta Function

Mahipal Gurram

We introduce a family of deformed Bailey pairs whose $q$ -series, which converge in a two-step limit ( $q \to 1^{-}$ followed by $n \to \infty$ ) to Dirichlet $L$ -functions scaled by $1…

math.GM2025

A Unified Transformation Formula for Ramanujan's Theta Function

Mahipal Gurram

In this paper, we derive a unified generalization of Ramanujan's transformation identities for the theta function $f (a, b)$ , originally appearing in Ramanujan's Notebooks, Parts~III…

math.NT2025

Generalized Cotangent Series and Links Zeta and Theta Functions

Mahipal Gurram

This paper develops a generalized cotangent-type series, extending classical expansions to higher-order lattice sums. By introducing a new family of series indexed by integer power…

math.NT2025

A New Representation of the Riemann Zeta Function

Mahipal Gurram

In this paper,we develop a novel representation of the zeta function expressed as the limiting difference between two structured double sums. This approach leads to a new and elega…

Explicit Lower Bounds for Dirichlet Series of Higher Power Representation Functions

Bailey-Zeta Limits: A q-Series Bridge to Dirichlet L-Functions and the Riemann Zeta Function

A Unified Transformation Formula for Ramanujan's Theta Function

Generalized Cotangent Series and Links Zeta and Theta Functions

A New Representation of the Riemann Zeta Function

Bailey-Zeta Limits: A $q$ -Series Bridge to Dirichlet $L$ -Functions and the Riemann Zeta Function