List questions from analytic-number-theory

Published on 21 Jun 2023 - 5:53

140

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Prove that $-\int_{0}^{1}\frac{{\rm Li}_2(-x(1-x))}{x}\ dx=\frac{2}{5}\zeta(3)$

Published on 27 Mar 2026 - 7:50

99

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How to prove this relationship between $\log\zeta(s)$ and prime counting function proposed in Riemann's paper?

Published on 03 Apr 2026 - 1:46

122

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A few questions about Riemann's Main Formula in the paper On the Number of Primes Less Than a Given Magnitude

Published on 29 Mar 2026 - 8:45

82

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Perron's Formula with $\rm{si}$-Remainder

Published on 25 Mar 2026 - 17:18

69

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Let $f(x)$ be a non-negative decreasing function, goes to 0, what can we say about the asymptotic behaviour of $\sum_{p \leq x} f(p)$?

Published on 03 Jul 2023 - 5:39

44

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Changing the order of integration and splitting the two integrals.

Published on 06 Jul 2023 - 1:35

125

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How to interpret this sum in Tate's thesis?

Published on 08 Jul 2023 - 15:50

100

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Elegant Papers in analytic number theory such as Thomas Wright

Published on 23 Feb 2026 - 3:26

33

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Showing $\sum_{p^k\le x}{k\ge 2} = O(1/p^2)$

Published on 12 Jul 2023 - 10:14

60

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Adding a square to a number gives a prime

Published on 12 Jul 2023 - 14:27

51

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Swapping finite product with infinite sum

Published on 12 Jul 2023 - 15:11

134

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swapping infinite sum with the logarithm for the logarithm with the infinite product

Published on 30 Mar 2026 - 5:15

92

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Question about proof of the truncated Perron's formula dealing with bounds and convergence

Published on 27 Mar 2026 - 2:35

40

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LCM sum with $\log $'s

Published on 26 Mar 2026 - 6:09

List Question

Sum of Three Primes and Vinogradov's Theorem

Prove that $-\int_{0}^{1}\frac{{\rm Li}_2(-x(1-x))}{x}\ dx=\frac{2}{5}\zeta(3)$

How to prove this relationship between $\log\zeta(s)$ and prime counting function proposed in Riemann's paper?

A few questions about Riemann's Main Formula in the paper On the Number of Primes Less Than a Given Magnitude

Perron's Formula with $\rm{si}$-Remainder

Let $f(x)$ be a non-negative decreasing function, goes to 0, what can we say about the asymptotic behaviour of $\sum_{p \leq x} f(p)$?

Changing the order of integration and splitting the two integrals.

How to interpret this sum in Tate's thesis?

Elegant Papers in analytic number theory such as Thomas Wright

Showing $\sum_{p^k\le x}{k\ge 2} = O(1/p^2)$

Adding a square to a number gives a prime

Swapping finite product with infinite sum

swapping infinite sum with the logarithm for the logarithm with the infinite product

Question about proof of the truncated Perron's formula dealing with bounds and convergence

LCM sum with $\log $'s

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