List questions from analytic-number-theory

Published on 25 Mar 2026 - 23:52

469

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Dirichlet series for $\zeta^3(s)/\zeta(2s)$.

Published on 14 Apr 2026 - 1:03

72

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Triangle inequality of Dirichlet cofficients of Artin L-function.

Published on 25 Mar 2026 - 23:52

199

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$p$-adic valuations of infinite products

Published on 12 Apr 2026 - 18:33

264

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Why do sieves have the parity problem?

Published on 11 Apr 2026 - 20:35

63

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Average order of $\frac{d(n)}{n^\alpha}$ where $\alpha>0,\alpha\neq 1$.

Published on 26 Apr 2026 - 1:12

83

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Finding expression for $\sum\limits_{n\leq x}\frac{\varphi(n)}{n^\alpha}$.

Published on 17 Apr 2026 - 11:09

124

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union of locally convergent domains regarding $\zeta(s)=\sum1/n^s$

Published on 16 Apr 2026 - 0:41

308

Views

Region of convergence of the Laplace transform.

Published on 16 Apr 2026 - 3:00

244

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Why are there more prime factors of the form $4k-1$ than of the form $4k+1$?

Published on 15 Apr 2026 - 19:15

78

Views

proving that dirichlet series has non negative coefficients and does not converge for all $s\in\mathbb{C}$

Published on 16 Apr 2026 - 17:18

200

Views

Sum over primitive Dirichlet characters

Published on 09 Apr 2026 - 16:36

61

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How to regularize $1 - 2 + 0 + 4 - 5 + 0 + 7 - 8 + 0 + \dots $?

Published on 16 Apr 2026 - 8:15

56

Views

If $f(p^r) = c(c+1)^{r−1}$ for all prime powers $p^r$, then $F(n) = ∑_{d|n} f(d)$ is completely multiplicative.

Published on 17 Apr 2026 - 3:18

198

Views

Logarithmic average of the Legendre symbol

Published on 25 Mar 2026 - 23:53

List Question

Why is $s=1$ in Dirichlet's Class Number Fomula when $L$-functions are only defined for $\Re(s)>1$?

Dirichlet series for $\zeta^3(s)/\zeta(2s)$.

Triangle inequality of Dirichlet cofficients of Artin L-function.

$p$-adic valuations of infinite products

Why do sieves have the parity problem?

Average order of $\frac{d(n)}{n^\alpha}$ where $\alpha>0,\alpha\neq 1$.

Finding expression for $\sum\limits_{n\leq x}\frac{\varphi(n)}{n^\alpha}$.

union of locally convergent domains regarding $\zeta(s)=\sum1/n^s$

Region of convergence of the Laplace transform.

Why are there more prime factors of the form $4k-1$ than of the form $4k+1$?

proving that dirichlet series has non negative coefficients and does not converge for all $s\in\mathbb{C}$

Sum over primitive Dirichlet characters

How to regularize $1 - 2 + 0 + 4 - 5 + 0 + 7 - 8 + 0 + \dots $?

If $f(p^r) = c(c+1)^{r−1}$ for all prime powers $p^r$, then $F(n) = ∑_{d|n} f(d)$ is completely multiplicative.

Logarithmic average of the Legendre symbol

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