Question

How to show that $O(\sum_1^{\infty} n^{1-{2\sigma}} e^{-\delta n} \sum_1^{n/2} 1/r )=O({\delta}^{2 \sigma -2} \log \dfrac{1}{\delta})$?

score 41 · Answer 1 · 2026-03-31 13:02:08

41

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How to show that $O(\sum_1^{\infty} n^{1-{2\sigma}} e^{-\delta n} \sum_1^{n/2} 1/r )=O({\delta}^{2 \sigma -2} \log \dfrac{1}{\delta})$?

Published on 31 Mar 2026 - 13:02

score 45 · Answer 2 · 2026-03-31 18:20:50

45

Views

Regularization of $\lim_{n\to\infty}n^s$ using Zeta Function

Published on 31 Mar 2026 - 18:20

score 60 · Answer 3 · 2026-03-26 17:47:42

60

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Analytic continuation of Bernoulli numbers: $B_{1/2}$?

Published on 26 Mar 2026 - 17:47

score 17 · Answer 4 · 2026-03-13 12:18:27

17

Views

Understanding the Theorem in Sec . 7.8. of Titchmarsh's Book

Published on 13 Mar 2026 - 12:18

score 113 · Answer 5 · 2026-03-25 17:51:41

113

Views

A Conjecture Relating Modulo Arithmetic and the Riemann Zeta Function.

Published on 25 Mar 2026 - 17:51

score 89 · Answer 6 · 2026-03-31 12:58:01

89

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Corollary 1.17 in Montgomery & Vaughan's Multiplicative Number Theory

Published on 31 Mar 2026 - 12:58

score 139 · Answer 7 · 2024-02-24 08:53:10

139

Views

Roots of $f(z)=z^2$

Published on 24 Feb 2024 - 8:53

score 99 · Answer 8 · 2026-03-29 15:16:47

99

Views

Proper Way to Calculate Value of Riemann Zeta function?

Published on 29 Mar 2026 - 15:16

score 40 · Answer 9 · 2026-03-26 09:40:31

40

Views

Two slightly different polynomial expansions for $\Xi(0)$. Could a connection between these two be derived?

Published on 26 Mar 2026 - 9:40

score 36 · Answer 10 · 2026-03-26 07:40:33

36

Views

Denjoy's Probabilistic Interpretation

Published on 26 Mar 2026 - 7:40

score 118 · Answer 11 · 2024-02-26 18:04:14

118

Views

Bounds on number of primes $<n$ by re-examining Euler's function

Published on 26 Feb 2024 - 18:04

score 63 · Answer 12 · 2024-02-26 20:48:44

63

Views

Calculating $\dfrac{d^{m-1}}{ds^{m-1}} \Big(\dfrac{\zeta'(s)}{\zeta(s)} \Big)$

Published on 26 Feb 2024 - 20:48

score 28 · Answer 13 · 2026-03-31 15:14:32

28

Views

Show that $\dfrac{d^{m-1}}{ds^{m-1}} \Big(\dfrac{\zeta'(s)}{\zeta(s)} \Big) =- \sum_{|\gamma -t|<1} \dfrac{1}{(s-\rho)^m} + \mathcal{O} (\log t)$.

Published on 31 Mar 2026 - 15:14

score 36 · Answer 14 · 2024-02-27 01:11:53

36

Views

where are the poles in the product of zeta functions, and where are their residues?

Published on 27 Feb 2024 - 1:11

score 85 · Answer 15 · 2024-03-02 04:05:50

85

Views

How to show that $\sum_{\rho} 1/|\rho| = \infty$?

Published on 02 Mar 2024 - 4:05

List Question

How to show that $O(\sum_1^{\infty} n^{1-{2\sigma}} e^{-\delta n} \sum_1^{n/2} 1/r )=O({\delta}^{2 \sigma -2} \log \dfrac{1}{\delta})$?

Regularization of $\lim_{n\to\infty}n^s$ using Zeta Function

Analytic continuation of Bernoulli numbers: $B_{1/2}$?

Understanding the Theorem in Sec . 7.8. of Titchmarsh's Book

A Conjecture Relating Modulo Arithmetic and the Riemann Zeta Function.

Corollary 1.17 in Montgomery & Vaughan's Multiplicative Number Theory

Roots of $f(z)=z^2$

Proper Way to Calculate Value of Riemann Zeta function?

Two slightly different polynomial expansions for $\Xi(0)$. Could a connection between these two be derived?

Denjoy's Probabilistic Interpretation

Bounds on number of primes $<n$ by re-examining Euler's function

Calculating $\dfrac{d^{m-1}}{ds^{m-1}} \Big(\dfrac{\zeta'(s)}{\zeta(s)} \Big)$

Show that $\dfrac{d^{m-1}}{ds^{m-1}} \Big(\dfrac{\zeta'(s)}{\zeta(s)} \Big) =- \sum_{|\gamma -t|<1} \dfrac{1}{(s-\rho)^m} + \mathcal{O} (\log t)$.

where are the poles in the product of zeta functions, and where are their residues?

How to show that $\sum_{\rho} 1/|\rho| = \infty$?

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