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arXiv · 1809.06921

Special values of derivatives of $L$-series and generalized Stieltjes constants

M. Ram Murty·Siddhi Pathak
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Abstract

The connection between derivatives of $L(s,f)$ for periodic arithmetical functions $f$ at $s=1$ and generalized Stieltjes constants has been noted earlier. In this paper, we utilize this link to throw light on the arithmetic nature of $L'(1,f)$ and certain Stieltjes constants. In particular, if $p$ is an odd prime greater than $7$, then we deduce the transcendence of at least $(p-7)/2$ of the generalized Stieltjes constants, $\{ γ_1(a,p) : 1 \leq a < p \}$, conditional on a conjecture of S. Gun, M. R. Murty and P. Rath.

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M. Ram Murty, Siddhi Pathak. 2018-09-18. Special values of derivatives of $L$-series and generalized Stieltjes constants. https://doi.org/10.4064/aa170615-13-3

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