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arXiv · 2512.18502

Explicit Lower Bounds for Dirichlet Series of Higher Power Representation Functions

Mahipal Gurram
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Abstract

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 combining generalized theta generating functions with a family of generalized cotangent series introduced in previous work, we derive two distinct explicit lower bounds for these series. The first estimate arises from a geometric restriction of the lattice to its diagonal, while the second utilizes Holder's inequality on the integral representation of the series. The methods presented here avoid modular techniques and offer a flexible analytic framework for higher-power representation problems.

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Mahipal Gurram. 2025-12-20. Explicit Lower Bounds for Dirichlet Series of Higher Power Representation Functions. https://arxiv.org/abs/2512.18502

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