List questions from analytic-number-theory

Published on 30 Mar 2026 - 0:19

52

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Bound the sum $\sum_{n=1, n \neq x}^{\infty} |a_n|(\frac{x}{n})^c \min (1, \frac{1}{R|\log \frac{x}{n}|}) $

Published on 01 Apr 2026 - 23:10

160

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Goldbach for almost primes

Published on 15 May 2023 - 12:19

85

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Mellin transform triads

Published on 25 Mar 2026 - 17:16

206

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Show $\sum_p\frac{1}{p^{1+i}}$ converges

Published on 17 May 2023 - 7:27

263

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Why do number theorists care so much about how well $\text{Li}(x)$ approximates $\pi(x)$ if it's not our best approximation?

Published on 23 Feb 2026 - 8:41

175

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Why is the Riemann explicit formula for primes (via the Riemann Hypothesis) any better than existing formulae?

Published on 23 Feb 2026 - 8:41

37

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Voronoi summation formula with Dirichlet character

Published on 18 May 2023 - 11:56

21

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Do Dirichlet $L$-functions with greater modulus have a greater number of zeros lying off the critical line?

Published on 18 May 2023 - 15:02

118

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A problem on von Mangoldt function.

Published on 27 Mar 2026 - 6:15

192

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Analytic continuation of a series $\Psi(s)$?

Published on 26 Mar 2026 - 11:04

132

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How well does $\mathrm{Zi}(x)=\frac1e\sum_{k=1}^\infty\frac{(\ln x)^k}{kk!\phi(k)}$, with $\phi(k)=\sum_{n=1}^\infty e^{-n^k}$, approximate $\pi(x)$?

Published on 20 May 2023 - 22:18

37

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Zero Free Region of $\zeta(s)$

Published on 21 May 2023 - 17:43

231

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A general theorem concerning arithmetic functions

Published on 25 Mar 2026 - 14:28

72

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conclusion of simple pole of $ -\frac{\zeta'(s)}{\zeta(s)}$

Published on 02 Apr 2026 - 23:59

List Question

Lambert series and higher order derivatives of the Euler Function

Bound the sum $\sum_{n=1, n \neq x}^{\infty} |a_n|(\frac{x}{n})^c \min (1, \frac{1}{R|\log \frac{x}{n}|}) $

Goldbach for almost primes

Mellin transform triads

Show $\sum_p\frac{1}{p^{1+i}}$ converges

Why do number theorists care so much about how well $\text{Li}(x)$ approximates $\pi(x)$ if it's not our best approximation?

Why is the Riemann explicit formula for primes (via the Riemann Hypothesis) any better than existing formulae?

Voronoi summation formula with Dirichlet character

Do Dirichlet $L$-functions with greater modulus have a greater number of zeros lying off the critical line?

A problem on von Mangoldt function.

Analytic continuation of a series $\Psi(s)$?

How well does $\mathrm{Zi}(x)=\frac1e\sum_{k=1}^\infty\frac{(\ln x)^k}{kk!\phi(k)}$, with $\phi(k)=\sum_{n=1}^\infty e^{-n^k}$, approximate $\pi(x)$?

Zero Free Region of $\zeta(s)$

A general theorem concerning arithmetic functions

conclusion of simple pole of $ -\frac{\zeta'(s)}{\zeta(s)}$

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