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Tushar Karmakar

Publications and source records attributed to Tushar Karmakar.

2 recordsLinked to original sources
arXiv2026

Riesz Means of Quadratic Class Numbers

We prove an asymptotic formula for a weighted Riesz mean of Hurwitz class numbers and real quadratic class numbers. To do this, we introduce L-functions for weight $\frac {1}{2} $ sesquiharmonic Maass forms of moderate growth and prove a formula for the Riesz means of the corresponding generalized mock modular forms, generalizing a recent result of the first author with Diamantis, Gupta, Rolen, and Thalagoda for mock modular forms. We then apply this formula to a sesquiharmonic Maass form that was first introduced by Duke, Imamoglu, and Tóth.

math.NT↗
arXiv2024

Laurent series expansions of $L$-functions

One of the main objectives of the current paper is to revisit the well known Laurent series expansions of the Riemann zeta function $ζ(s)$, Hurwitz zeta function $ζ(s,a)$ and Dirichlet $L$-function $L(s,χ)$ at $s=1$. Moreover, we also present a new Laurent series expansion of $L$-functions associated to cusp forms over the full modular group.

math.NT↗