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Closed form for $\sum_{n=1}^\infty\binom{2n}{n}\zeta(m,n+1)x^n$

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#sequences-and-series #binomial-coefficients #special-functions #closed-form #zeta-functions
53
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Is there a mistake in Zagier's "Hyperbolic manifolds and special values of Dedekind zeta-functions"?

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#number-theory #hyperbolic-geometry #quaternions #geodesic #zeta-functions
32
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Precomposing local L functions with $p^{-x}$

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#number-theory #algebraic-geometry #zeta-functions
71
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Converting polylogarithms to Dirichlet L functions

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#zeta-functions #polylogarithm #l-functions #dirichlet-character
71
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Function $\mathcal{Z}\left(x\right)=\sum_{n=1}^{\infty}n^{-x}\sin\left(n\right)$

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#calculus #integration #summation #riemann-zeta #zeta-functions
60
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Is the function $F(s)= \int_{\gamma_{\epsilon}} \frac{z^{s-1}}{e^{z}-1} \ dz$ analytic?

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#complex-analysis #analytic-functions #zeta-functions
111
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Zeros of Riemann's $\xi(t)$

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#analytic-number-theory #riemann-zeta #zeta-functions
67
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Cancelling terms in an infinite series over $\mathbb{N}^2$

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#sequences-and-series #recurrence-relations #zeta-functions
168
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Analytic continuation of Dirichlet beta funcion

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#contour-integration #zeta-functions #beta-function
49
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Zeta functions of hyperelliptic curves

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#algebraic-geometry #finite-fields #algebraic-curves #zeta-functions
120
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If $n\in\mathbb N$, then $\sum_{k=1}^{\infty} \frac{1}{k^n}$ diverges. What's wrong in my proof?

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#sequences-and-series #algebra-precalculus #divergent-series #zeta-functions
80
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An integral similar to Abel Plana: $\displaystyle \int_{0}^{\infty}{\dfrac{\ln(1+x^2)}{e^{2πnx}-1}}\ \mathrm{d}x\\ $

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#definite-integrals #special-functions #zeta-functions
28
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A certain formal power series equals the zeta function of a curve

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#representation-theory #finite-fields #zeta-functions #formal-power-series
277
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Explore the relationship between $\sum\limits_{n = 1}^{2x} \frac{1}{{n^s}^x}$ and $\sum\limits_{n = 1}^{2x-1} \frac{(-1)^{n-1}}{{n^s}^x}$

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#number-theory #roots #riemann-zeta #zeta-functions #dirichlet-series
18
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$ f(s) = 1 + \sum_{n=2}^{\infty} \frac{n^{-s}}{p_n}= 0$?

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#prime-numbers #roots #zeta-functions #analytic-continuation #dirichlet-series

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