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Alternating Bertrand series

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#summation #logarithms #zeta-functions #dirichlet-series
93
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Prove the series $\sum n^{-1-it}$ is diverge for all real $t$.

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#analytic-number-theory #zeta-functions #dirichlet-series
109
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Help with the derivation of the class number formula

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#ring-theory #dirichlet-series #ideal-class-group
117
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Squared modulus of Dirichlet eta function.

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#complex-analysis #special-functions #dirichlet-series
2.8k
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What is the limit of this Dirichlet series?

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#sequences-and-series #number-theory #limits #analysis #dirichlet-series
185
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A formula to find $ \lim_{s \to 1} \frac{1}{\zeta(s)} (\sum_{x_i=1}^\infty \dots \sum_{x_1 =1}^\infty)\frac{1}{ (\sum_{k=1}^i (x_k)^i)^s}$?

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#sequences-and-series #number-theory #dirichlet-series
47
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Extension of an identity related to a Dirichlet series

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#complex-analysis #number-theory #dirichlet-series
404
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Convergence of $\sum_{n=1}^\infty\frac{\cot \varphi\pi n}{n^s}$

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#sequences-and-series #number-theory #convergence-divergence #diophantine-approximation #dirichlet-series
114
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Question about Dirichlet Series Related to Formula for $\frac{1}{e}$

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#number-theory #riemann-zeta #dirichlet-series #mobius-function #mellin-transform
800
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Meaning of absolute constant

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#complex-analysis #number-theory #definition #analytic-number-theory #dirichlet-series
214
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Generalising the Dirichlet L-Series

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#analytic-number-theory #dirichlet-series
244
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$\sum_{n=1}^\infty \chi(n)\phi(n)n^{-s} = \frac{L(\chi,s-1)}{L(\chi,s)}$

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#number-theory #dirichlet-series
436
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Precise factorization of Dedekind zeta function of cyclotomic field

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#number-theory #algebraic-number-theory #dirichlet-series #cyclotomic-fields
433
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Inversion theorem for Dirichlet series

Published on
#dirichlet-series #dirichlet-convolution
236
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An asymptotic series for $\small\prod_{k=n}^\infty\operatorname{sinc}\left({2^{-k}}\pi\right),\,n\to\infty$

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#asymptotics #infinite-product #conjectures #dirichlet-series #experimental-mathematics

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