List questions from analytic-number-theory

Published on 26 Mar 2026 - 16:06

102

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Does the average reciprocal of the smallest or largest prime factors of integers converge?

Published on 03 Jul 2019 - 5:42

145

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Density of Numbers with Exactly One Prime Factor of Multiplicity 1

Published on 23 Feb 2026 - 4:56

171

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Minimum and maximum of a partial Euler product?

Published on 25 Mar 2026 - 9:47

254

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Is $\sum_{n=1}^{\infty} \frac{\mu(n)}{n} = 0$?

Published on 09 Jul 2019 - 1:14

40

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Probability for an L-function to be RS-primitive

Published on 25 Mar 2026 - 9:53

99

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Why is the series representation of the logarithm of the zeta function analytic?

Published on 29 Mar 2026 - 19:17

41

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Can a upper bound of $\sum_{b=1}^{p-1}\left(\frac{b^2-a^2}{p}\right)\left(\frac{b^2-1}{p}\right)$, $a\in{Z}$, be strictly less than $\sqrt{p}$?

Published on 26 Mar 2026 - 3:13

46

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Show, $\sum_{\chi\neq\chi_0}(\sum_{a=2}^{p-2}\sum_{b=1}^{p-1}\chi(a)(\frac{b^2-a^2}{p})(\frac{b^2-1}{p}))^2|L(1,\chi)|=O(p^{7/2}\log p)$.

Published on 12 Jul 2019 - 18:26

636

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Relationship between GCD, LCM and the Riemann Zeta function

Published on 14 Jul 2019 - 19:22

18

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Is the following equality concerning an $L$-function really true?

Published on 22 Mar 2026 - 19:57

299

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Are there infinitely many zeroes of $\sum_{r = 1}^{n-1} \mu(r)\gcd(n,r) $?

Published on 27 Mar 2026 - 4:35

159

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sign unchanged for Dirichlet polynomials?

Published on 25 Mar 2026 - 9:34

337

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Why logarithmic density of sets are studied?

Published on 31 Mar 2026 - 22:24

118

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Diophantine approximation and Farey sequences

Published on 23 Mar 2026 - 5:27

List Question

Weyl's equidistribution theorem in the case of rational numbers

Does the average reciprocal of the smallest or largest prime factors of integers converge?

Density of Numbers with Exactly One Prime Factor of Multiplicity 1

Minimum and maximum of a partial Euler product?

Is $\sum_{n=1}^{\infty} \frac{\mu(n)}{n} = 0$?

Probability for an L-function to be RS-primitive

Why is the series representation of the logarithm of the zeta function analytic?

Can a upper bound of $\sum_{b=1}^{p-1}\left(\frac{b^2-a^2}{p}\right)\left(\frac{b^2-1}{p}\right)$, $a\in{Z}$, be strictly less than $\sqrt{p}$?

Show, $\sum_{\chi\neq\chi_0}(\sum_{a=2}^{p-2}\sum_{b=1}^{p-1}\chi(a)(\frac{b^2-a^2}{p})(\frac{b^2-1}{p}))^2|L(1,\chi)|=O(p^{7/2}\log p)$.

Relationship between GCD, LCM and the Riemann Zeta function

Is the following equality concerning an $L$-function really true?

Are there infinitely many zeroes of $\sum_{r = 1}^{n-1} \mu(r)\gcd(n,r) $?

sign unchanged for Dirichlet polynomials?

Why logarithmic density of sets are studied?

Diophantine approximation and Farey sequences

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