Question

Non-vanishing of Dirichlet $L$-function $L(s,\chi)$ for $\Re(s)=1$

score 153 · Answer 1 · 2026-03-25 11:26:26

153

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Non-vanishing of Dirichlet $L$-function $L(s,\chi)$ for $\Re(s)=1$

Published on 25 Mar 2026 - 11:26

score 128 · Answer 2 · 2026-03-28 20:37:47

128

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Let $\frac{r}{2t}\in\mathbb{Q}$ with $r,t$ odd, then $\frac{r}{2t}\in\Gamma_1(4)*\frac{1}{2}$ with $\Gamma_1(4)$ a principal subgroup.

Published on 28 Mar 2026 - 20:37

score 96 · Answer 3 · 2020-03-07 11:08:18

96

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Application and generalisation of Ikehara's tauberian theorem

Published on 07 Mar 2020 - 11:08

score 62 · Answer 4 · 2026-03-27 00:04:19

62

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How to check if the series is analytic?

Published on 27 Mar 2026 - 0:04

score 88 · Answer 5 · 2026-03-25 22:05:29

88

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What is known on the sum $\sum_{N\le n\le 2N}\dfrac{\mu(n)n^{it}}{\sqrt{n}}$?

Published on 25 Mar 2026 - 22:05

score 244 · Answer 6 · 2020-03-08 11:11:37

244

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Puzzled by this heuristic argument for the prime number theorem

Published on 08 Mar 2020 - 11:11

score 91 · Answer 7 · 2020-03-10 12:44:07

91

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How to obtain an upper bound for $\sum_{d|n} d \sum_{m|d} m$?

Published on 10 Mar 2020 - 12:44

score 119 · Answer 8 · 2026-03-25 20:08:37

119

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Ramanujan primes in short intervals

Published on 25 Mar 2026 - 20:08

score 189 · Answer 9 · 2020-03-14 11:47:57

189

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Why is $\sum_{n \leq x }1/n=\log(x)+\mathcal{O(1)}$?

Published on 14 Mar 2020 - 11:47

score 46 · Answer 10 · 2020-03-14 19:18:17

46

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Inequalities $\pi(x^a+y^b)^\alpha\leq \pi(x^c)^\beta+\pi(y^d)^\gamma$ involving the prime-counting function, where the constants are very close to $1$

Published on 14 Mar 2020 - 19:18

score 41 · Answer 11 · 2026-03-25 06:02:25

41

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Sign of a function that involves the arithmetic function that counts the number of Ramanujan primes less than a given integer

Published on 25 Mar 2026 - 6:02

score 76 · Answer 12 · 2026-03-26 12:33:56

76

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Prime counting formula considered by S.Wigert

Published on 26 Mar 2026 - 12:33

score 145 · Answer 13 · 2026-04-01 05:14:52

145

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Infinite product $\prod_p (1+p^{-2}+p^{-3} +\dots+p^{-k})$

Published on 01 Apr 2026 - 5:14

score 74 · Answer 14 · 2020-03-17 07:37:10

74

Views

Unable to think why integral should be convergent

Published on 17 Mar 2020 - 7:37

score 178 · Answer 15 · 2020-03-17 15:52:27

178

Views

On the inequality $\left(\frac{R_{n+1}}{R_n}\right)^n<n^{\frac{5}{4}}(\log n)^3$ for Ramanujan primes

Published on 17 Mar 2020 - 15:52

List Question

Non-vanishing of Dirichlet $L$-function $L(s,\chi)$ for $\Re(s)=1$

Let $\frac{r}{2t}\in\mathbb{Q}$ with $r,t$ odd, then $\frac{r}{2t}\in\Gamma_1(4)*\frac{1}{2}$ with $\Gamma_1(4)$ a principal subgroup.

Application and generalisation of Ikehara's tauberian theorem

How to check if the series is analytic?

What is known on the sum $\sum_{N\le n\le 2N}\dfrac{\mu(n)n^{it}}{\sqrt{n}}$?

Puzzled by this heuristic argument for the prime number theorem

How to obtain an upper bound for $\sum_{d|n} d \sum_{m|d} m$?

Ramanujan primes in short intervals

Why is $\sum_{n \leq x }1/n=\log(x)+\mathcal{O(1)}$?

Inequalities $\pi(x^a+y^b)^\alpha\leq \pi(x^c)^\beta+\pi(y^d)^\gamma$ involving the prime-counting function, where the constants are very close to $1$

Sign of a function that involves the arithmetic function that counts the number of Ramanujan primes less than a given integer

Prime counting formula considered by S.Wigert

Infinite product $\prod_p (1+p^{-2}+p^{-3} +\dots+p^{-k})$

Unable to think why integral should be convergent

On the inequality $\left(\frac{R_{n+1}}{R_n}\right)^n<n^{\frac{5}{4}}(\log n)^3$ for Ramanujan primes

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