List questions from analytic-number-theory

Published on 25 Mar 2026 - 14:32

74

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coefficient $[q^n]\sum_{m\ge1}\frac{q^{\alpha m}}{1-q^{\beta m}}$ where $0<\alpha<\beta$

Published on 25 Mar 2026 - 14:34

69

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Two questions about the infinitude of prime Euclid numbers: $E_{n}=p_{1}\cdot p_{2}\cdot \ldots \cdot p_{n} + 1$

Published on 16 Apr 2026 - 0:40

205

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Prove that the following statement involving Buchstab function is true

Published on 12 Apr 2026 - 18:52

173

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Is this some sort of modular form? $f(\tau)=\eta(a\tau)\eta(b\tau)$

Published on 25 Mar 2026 - 16:08

64

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Need Help understanding the philosophy behind splitting the integrals into sqrt(x)

Published on 09 Apr 2026 - 14:14

90

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Techniques of estimating integrals, asymptotic behavior of Li(x)

Published on 14 Apr 2026 - 15:12

196

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Chebyshev’s $\theta_1(x) = \sum_{n \leqslant x } (x-n) \Lambda_1 (n)$

Published on 16 Apr 2026 - 15:09

183

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Properties of Chebyshev’s $\psi$ Function

Published on 09 Apr 2026 - 2:10

46

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Do we have $\nu_t (t!) = o(t)$?

Published on 13 Apr 2026 - 23:56

129

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Prove $\sum_{n\le x} d(n)/n = \frac12 \log^2 x + 2e \log x + c + \mathcal O(1/\sqrt{x})$ where $d$ is the divisor function and $c$ is a constant

Published on 17 Apr 2026 - 3:43

61

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Possible alternate proof of Bertrand's postulate.

Published on 14 Apr 2026 - 7:39

117

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Big Oh notation and inequality

Published on 14 Apr 2026 - 1:24

57

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Triviality in my proof of Bertrand's postulate.

Published on 13 Apr 2026 - 6:18

88

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A possible proof of the existence of a prime in the interval [n,2n].

Published on 14 Apr 2026 - 7:36

List Question

Symbolic calculation vs. desmos

coefficient $[q^n]\sum_{m\ge1}\frac{q^{\alpha m}}{1-q^{\beta m}}$ where $0<\alpha<\beta$

Two questions about the infinitude of prime Euclid numbers: $E_{n}=p_{1}\cdot p_{2}\cdot \ldots \cdot p_{n} + 1$

Prove that the following statement involving Buchstab function is true

Is this some sort of modular form? $f(\tau)=\eta(a\tau)\eta(b\tau)$

Need Help understanding the philosophy behind splitting the integrals into sqrt(x)

Techniques of estimating integrals, asymptotic behavior of Li(x)

Chebyshev’s $\theta_1(x) = \sum_{n \leqslant x } (x-n) \Lambda_1 (n)$

Properties of Chebyshev’s $\psi$ Function

Do we have $\nu_t (t!) = o(t)$?

Prove $\sum_{n\le x} d(n)/n = \frac12 \log^2 x + 2e \log x + c + \mathcal O(1/\sqrt{x})$ where $d$ is the divisor function and $c$ is a constant

Possible alternate proof of Bertrand's postulate.

Big Oh notation and inequality

Triviality in my proof of Bertrand's postulate.

A possible proof of the existence of a prime in the interval [n,2n].

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