List questions from analytic-number-theory

Published on 14 Apr 2026 - 18:03

319

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The average order of $\sigma(n)$.

Published on 12 Apr 2026 - 2:24

77

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Map $z^2=\frac{\frac{1}{2}+it}{ \frac{1}{2}-it },t\in\mathbb{R}$ maps the real axis $(-\infty,\infty)$ onto the unit circle $\mid z\mid=1$.

Published on 17 Apr 2026 - 14:23

87

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Where does $\frac{3}{2}$ in $1<s\cdot\zeta(s+1) < \frac{3}{2}$ come from?

Published on 15 Apr 2026 - 22:52

148

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Good bound for $\sum_{p\mid n}\frac{1}{p}$

Published on 17 Apr 2026 - 8:22

109

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Analysis of series containing Zeta function:

Published on 12 Apr 2026 - 8:42

71

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Prove$\sum_{|\alpha|<1, f(\alpha)=0}\log \frac{1}{|\alpha|}= \sum_{\Re(\rho)>1/2}\log\ |\frac{\rho}{1-\rho}|$

Published on 15 Apr 2026 - 20:17

238

Views

$f(z)=\frac{z}{1-z} \zeta(\frac {1}{1-z})$ belongs to Hardy Space $H^{1/3}(\mathbf{D})$

Published on 16 Apr 2026 - 6:56

43

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Estimate of smooth integers doesn't fit the actual graph

Published on 16 Apr 2026 - 13:46

103

Views

The number of ways an even integer can be written as the sum of two primes

Published on 10 Apr 2026 - 17:14

209

Views

Squarefree totient sum

Published on 11 Apr 2026 - 11:12

80

Views

Proof of Vaughan's identity, based on comparing the Dirichlet coefficients

Published on 14 Apr 2026 - 1:17

39

Views

Closed form of the sieve of Eratosthenes

Published on 12 Apr 2026 - 19:34

69

Views

$f(z)= (s-1) \zeta(s)$. Prove that $\log |f(0)|=0$

Published on 17 Apr 2026 - 5:31

102

Views

Why is Euler product destroyed?

Published on 17 Apr 2026 - 0:59

List Question

On Perron's formula with remainder

The average order of $\sigma(n)$.

Map $z^2=\frac{\frac{1}{2}+it}{ \frac{1}{2}-it },t\in\mathbb{R}$ maps the real axis $(-\infty,\infty)$ onto the unit circle $\mid z\mid=1$.

Where does $\frac{3}{2}$ in $1<s\cdot\zeta(s+1) < \frac{3}{2}$ come from?

Good bound for $\sum_{p\mid n}\frac{1}{p}$

Analysis of series containing Zeta function:

Prove$\sum_{|\alpha|<1, f(\alpha)=0}\log \frac{1}{|\alpha|}= \sum_{\Re(\rho)>1/2}\log\ |\frac{\rho}{1-\rho}|$

$f(z)=\frac{z}{1-z} \zeta(\frac {1}{1-z})$ belongs to Hardy Space $H^{1/3}(\mathbf{D})$

Estimate of smooth integers doesn't fit the actual graph

The number of ways an even integer can be written as the sum of two primes

Squarefree totient sum

Proof of Vaughan's identity, based on comparing the Dirichlet coefficients

Closed form of the sieve of Eratosthenes

$f(z)= (s-1) \zeta(s)$. Prove that $\log |f(0)|=0$

Why is Euler product destroyed?

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