6 papers
Bell Transforms of Arithmetic Functions: Euler Products, Congruences, and Polynomial Sequences
Mahipal Gurram
We present a unified algebraic framework utilizing the formal Bell transform to bridge the Dirichlet convolution of arithmetic functions with the combinatorial structure of infinit…
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…
Bailey-Zeta Limits: A -Series Bridge to Dirichlet -Functions and the Riemann Zeta Function
Mahipal Gurram
We introduce a family of deformed Bailey pairs whose -series, which converge in a two-step limit ( followed by ) to Dirichlet -functions scaled by $1…
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 , originally appearing in Ramanujan's Notebooks, Parts~III…
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…
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…