List questions from analytic-number-theory

Published on 19 Jan 2017 - 1:14

47

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$\pi(x)$ can not be expressed as quotient form of polynomial like that $\frac{P(x)}{Q(x)}$ where $P(x)$, $Q(x)$ are polynomials.

Published on 19 Jan 2017 - 5:30

67

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Does there exist an explicit formula that expresses $p_{n+1}-p_{n}$ in terms of $p_n$, the $n$th prime number?

Published on 25 Mar 2026 - 23:11

155

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Two exercises on characters on Marcus (part 1)

Published on 26 Mar 2026 - 16:57

173

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Two exercises on characters on Marcus (Part 2)

Published on 26 Mar 2026 - 20:25

121

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Why do the first two terms of Euler's summation by parts formula not cancel each other out?

Published on 25 Mar 2026 - 18:57

62

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the number of primitive roots of a modulo a fixed prime $p$ that are $\le x $

Published on 21 Jan 2017 - 14:15

233

Views

Integrals involving products of Bessel functions

Published on 30 Mar 2026 - 0:24

134

Views

Sum of fractional parts of linear and logarithmic functions

Published on 22 Jan 2017 - 1:55

92

Views

On coprime integers.

Published on 22 Jan 2017 - 8:09

95

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Proof of Dirichlet theorem with the help of $L(1,\chi)\neq 0$ for all $\chi\neq \chi_0$

Published on 22 Jan 2017 - 21:39

162

Views

Euler-Maclaurin summation formula for piecewise continuous functions

Published on 25 Mar 2026 - 4:36

1.2k

Views

A second course in modular forms

Published on 29 Mar 2026 - 15:51

457

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Property of Dirichlet character (Apostol 8.17)

Published on 23 Jan 2017 - 19:04

183

Views

Given a complete discrete valuation field $L$, is there always a complete local field $K\subset L$?

Published on 26 Mar 2026 - 13:51

List Question

Determination of class number formula

$\pi(x)$ can not be expressed as quotient form of polynomial like that $\frac{P(x)}{Q(x)}$ where $P(x)$, $Q(x)$ are polynomials.

Does there exist an explicit formula that expresses $p_{n+1}-p_{n}$ in terms of $p_n$, the $n$th prime number?

Two exercises on characters on Marcus (part 1)

Two exercises on characters on Marcus (Part 2)

Why do the first two terms of Euler's summation by parts formula not cancel each other out?

the number of primitive roots of a modulo a fixed prime $p$ that are $\le x $

Integrals involving products of Bessel functions

Sum of fractional parts of linear and logarithmic functions

On coprime integers.

Proof of Dirichlet theorem with the help of $L(1,\chi)\neq 0$ for all $\chi\neq \chi_0$

Euler-Maclaurin summation formula for piecewise continuous functions

A second course in modular forms

Property of Dirichlet character (Apostol 8.17)

Given a complete discrete valuation field $L$, is there always a complete local field $K\subset L$?

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