# Questions tagged [dirichlet-series]

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### A sharper estimate for a generalization of the sum-of-divisors function

I am interested in the function $f_n(m)$ which can be defined by the Dirichlet generating function $$\zeta(s)\zeta(s - 1) \cdots\zeta(s - n + 1) = \sum\limits_{m = 1}^\infty \frac{f_n(m)}{m^s}$$ This ...
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### Analyzing a Dirichlet series with log-oscillating terms via Fourier methods

I am investigating the series $S(z)$ defined as follows: $$S(z) = \sum_{n=1}^{\infty} n^{-a}\cos(b\ln(n)),$$ where $z = a + bi \in \mathbb{C}$, with $0 < a < 1$, and $b \in \mathbb{R}$. I want ...
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### Classification of L functions and Dirichlet series by poles

I am interested in the connection between particular Dirichlet series' abscissa of convergence and the poles of L-functions. Let $D(z) = \sum_{n=1}^\infty\frac{a_n}{n^z}$ be a Dirichlet series ...
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### Dirichlet series solution to Poisson Point Process question (repost from math.SE)

Reposting here because the bounty on the original math.SE post expired, with no solutions or comments received. For any discrete subset $S$ of $\mathbb{R}^d$, consider a digraph formed by placing an ...
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