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### A conjecture relating Multiple Zeta Values and the Polya Enumeration Theorem

Let me state my motivation. I believe that the Polya Enumeration Theorem and Multiple Zeta Values (the classic being the Basel problem and the values of the Riemann zeta function at the even ...
Riemann's zeta function is a function with many faces, I mean representations. I recently derived this one, bellow, as a continued fraction over prime numbers. \zeta(s)=1 ... 1answer 107 views ### Proof of a Dirichlet's theorem using the Riemann zeta function? Someone could tell me if there is a proof of the Dirichlet's theorem on arithmetic progressions stated below using only the Riemann zeta function \zeta(s)=\sum_{n=1}^\infty ... 1answer 306 views ### References to integrals of the form \int_{0}^{1} \left( \frac{1}{\log x}+\frac{1}{1-x} \right)^{m} \, dx While extending my calculation techniques, with aid of Mathematica, I found that \begin{align*} \int_{0}^{1}\left( \frac{1}{\log x} + \frac{1}{1-x} \right)^{3} \, dx &= -6 \zeta '(-1) ... 1answer 2k views ### Books about the Riemann Hypothesis I hope this question is appropriate for this forum. I am compiling a list of all books about the Riemann Hypothesis and Riemann's Zeta Function. Here is my list: The Riemann Hypothesis: A Resource ... 2answers 426 views ### Two Dirichlet's series related to the Divisor Summatory Function and to the Riemann's zeta-function, \zeta(s) Considering the \textit{Divisor Summatory Function}, D(n), defined as D(n) = \sum_{k=1}^{n}d(k) , $$where$$ d(n) = \sum_{k|n}^{n}1. $$One can observe the following pattern in the values of ... 1answer 253 views ### An infinite series involving the Zeta Function I am wondering if anyone knows how to evaluate either of the following sums in terms of known constants:$$\sum_{k=2}^{\infty}-\frac{\zeta^{'}(k)}{\zeta(k)}, and ...
This appears to be a relationship: $\sum\limits_{p\;\text{prime}} \frac{1}{p^s} = \log\zeta (s) - \sum\limits_{n=1}^{\infty}\frac{\sqrt{a_{n}b_{n}}}{n^{s}}$ where $a_{n}$ is a sequence of fractions ...