List questions from analytic-number-theory

44

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If the congruence $ x^2 \equiv n \bmod{P} $ has a solution then $(n \mid p_i) = 1 $ for each prime $ p_i $ that divides $ P $

Published on 16 Apr 2026 - 3:32

127

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Is there an asymptotic formula for primes in an arithmetic progression with the error terms?

Published on 11 Apr 2026 - 23:19

151

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Dirichlet L-series inequality

Published on 25 Mar 2026 - 9:23

166

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Dirichlet convolution of Mobius function with exponential function

Published on 26 Mar 2026 - 2:52

117

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Proving $\dfrac{4}{\pi}\sum_{k = 1}^{\infty}\dfrac{(-1)^{k - 1}k}{B_{2k}(2k - 1)}\left(\dfrac{\log n}{2\pi}\right)^{2k - 1} = \dfrac{n}{\text{In}n}$

Published on 16 Apr 2026 - 14:41

101

Views

What can we derive from an experimental plot of prime gap counts?

Published on 13 Apr 2026 - 17:31

68

Views

Proving Integral representation of $\zeta(n)$

Published on 12 Apr 2026 - 19:30

166

Views

Partial sum estimate for $\sum_{p\leq x} \frac{1}{p^{1/2}}$

Published on 14 Apr 2026 - 17:02

315

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On an integral related to the prime number theorem

Published on 14 Apr 2026 - 0:07

120

Views

The partial sums of $\log n$

Published on 13 Apr 2026 - 22:14

326

Views

On the Mellin transform of logarithmic integral

Published on 12 Apr 2026 - 6:04

218

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Distribution of prime gaps - is it an unsolved problem?

Published on 12 Apr 2026 - 4:02

120

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Improving Simple Probabilistic Prime Model To Model Prime Gaps

Published on 13 Apr 2026 - 14:35

42

Views

prime divisors of the sum of two integers with given prime divisors

Published on 17 Apr 2026 - 11:50

131

Views

About a sum over primes

Published on 11 Apr 2026 - 20:22

List Question

If the congruence $ x^2 \equiv n \bmod{P} $ has a solution then $(n \mid p_i) = 1 $ for each prime $ p_i $ that divides $ P $

Is there an asymptotic formula for primes in an arithmetic progression with the error terms?

Dirichlet L-series inequality

Dirichlet convolution of Mobius function with exponential function

Proving $\dfrac{4}{\pi}\sum_{k = 1}^{\infty}\dfrac{(-1)^{k - 1}k}{B_{2k}(2k - 1)}\left(\dfrac{\log n}{2\pi}\right)^{2k - 1} = \dfrac{n}{\text{In}n}$

What can we derive from an experimental plot of prime gap counts?

Proving Integral representation of $\zeta(n)$

Partial sum estimate for $\sum_{p\leq x} \frac{1}{p^{1/2}}$

On an integral related to the prime number theorem

The partial sums of $\log n$

On the Mellin transform of logarithmic integral

Distribution of prime gaps - is it an unsolved problem?

Improving Simple Probabilistic Prime Model To Model Prime Gaps

prime divisors of the sum of two integers with given prime divisors

About a sum over primes

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