User reuns

27 votes

Are there any series whose convergence is unknown?

answered Aug 9, 2017 at 11:23

26 votes

Accepted

What is this series relating to the residues of the Gamma function?

sequences-and-series special-functions gamma-function

answered Feb 13, 2017 at 22:53

24 votes

Riemann hypothesis: is Bender-Brody-Müller Hamiltonian a new line of attack?

eigenvalues-eigenvectors riemann-zeta riemann-hypothesis

answered Apr 5, 2017 at 21:40

21 votes

Accepted

How was the integral for Zeta Function created

integration summation riemann-zeta zeta-functions

answered Jul 4, 2016 at 18:46

20 votes

Accepted

how to prove that $1^x+2^x+3^x+4^x+\cdots+N^x$ will never sum to a prime number except $1^x+2^x$?

algebra-precalculus prime-numbers proof-explanation

answered May 1, 2021 at 4:53

17 votes

On proving that $\sum\limits_{n=1}^\infty \frac{n^{13}}{e^{2\pi n}-1}=\frac 1{24}$

sequences-and-series summation proof-writing pi summation-method

answered Feb 26, 2020 at 1:47

17 votes

Why isn't the directional derivative generally scaled down to the unit vector?

calculus multivariable-calculus derivatives vector-analysis

answered May 22, 2017 at 2:15

15 votes

The definition of "entire function"

complex-analysis functional-analysis analytic-number-theory

answered Aug 21, 2017 at 17:54

15 votes

Conjecture ${\large\int}_0^\infty\left[\frac1{x^4}-\frac1{2x^3}+\frac1{12\,x^2}-\frac1{\left(e^x-1\right)x^3}\right]dx=\frac{\zeta(3)}{8\pi^2}$

calculus integration definite-integrals closed-form experimental-mathematics

answered Jan 10, 2016 at 21:52

14 votes

Accepted

Is every Hilbert space separable?

functional-analysis hilbert-spaces inner-products

answered Sep 27, 2017 at 22:20

13 votes

Accepted

Explicit value for series

real-analysis sequences-and-series complex-analysis analysis

answered Oct 28, 2020 at 17:39

12 votes

Accepted

Does the Mertens function have an infinite number of zeros?

number-theory mobius-function

answered Jul 3, 2017 at 22:38

11 votes

$F(u) = F(u^2)$ if $u$ is algebraic of odd degree

abstract-algebra polynomials proof-verification field-theory

answered Jul 25, 2017 at 2:18

11 votes

Is an ideal finitely generated if its radical is finitely generated?

abstract-algebra commutative-algebra ideals examples-counterexamples

answered Feb 28, 2021 at 18:04

11 votes

Why is proving the Riemann Hypothesis so hard?

soft-question analytic-number-theory riemann-zeta riemann-hypothesis open-problem

answered Mar 6, 2021 at 11:05

10 votes

Accepted

Does a definite integral equal to the Möbius function exist?

complex-analysis number-theory

answered Jul 24, 2019 at 20:52

10 votes

Accepted

Torus and Elliptic curves

complex-analysis elliptic-curves elliptic-functions

answered Jul 23, 2017 at 18:32

10 votes

Proving that $F(x)=\sum\limits_{k=1}^{p-1}\left(\frac{k}{p}\right)x^k$ has at least $\frac{p-1}{2}$ different complex roots

number-theory polynomials

answered Dec 26, 2021 at 14:35

10 votes

A probably wrong proof of the Riemann Hypothesis, but where is the mistake?

proof-verification analytic-number-theory riemann-zeta riemann-hypothesis

answered Aug 27, 2019 at 11:49

9 votes

Accepted

Infinite series involving Von Mangoldt's function

sequences-and-series number-theory analytic-number-theory

answered Sep 10, 2017 at 16:44

9 votes

Does this sum of prime numbers converge?

convergence-divergence summation prime-numbers riemann-sum

answered Jun 16, 2017 at 18:20

9 votes

Accepted

Alternating series test for complex series

sequences-and-series complex-analysis analytic-continuation

answered Apr 17, 2016 at 20:12

8 votes

Relationship between GCD, LCM and the Riemann Zeta function

number-theory elementary-number-theory summation prime-numbers analytic-number-theory

answered Jul 14, 2019 at 20:32

8 votes

On the general form of the family $\sum_{n=1}^\infty \frac{n^{k}}{e^{2n\pi}-1} $

sequences-and-series closed-form gamma-function bernoulli-numbers

answered Jun 25, 2019 at 11:21

8 votes

Is $\int\limits_0^\infty\frac{\sin y}{y^{s+1}}dy=-\Gamma(-s)\sin(\frac{\pi s}{2})$ for $\operatorname{Re}(s)\in (-1,0)$ obvious?

real-analysis complex-analysis number-theory analysis

answered Dec 30, 2018 at 21:41

8 votes

Unsolved problems in Fourier analysis

fourier-analysis fourier-series

answered Apr 27, 2017 at 6:56

8 votes

Accepted

Euler Product formula for Riemann zeta function proof

sequences-and-series complex-analysis analytic-number-theory riemann-zeta euler-product

answered Apr 14, 2016 at 21:30

8 votes

Which derivatives are eventually periodic?

calculus derivatives

answered Feb 9, 2016 at 1:41

8 votes

Zeta of 3, why cant we get the value the zeta of odd n?

riemann-zeta zeta-functions

answered Oct 21, 2016 at 15:39

8 votes

$\lim_{n \to \infty}\frac{1}{n}\sum_{k = 1}^nf(k)$ where $f(n)$ is the largest prime factor exponent?

limits number-theory elementary-number-theory analytic-number-theory prime-factorization

answered Dec 25, 2021 at 15:24

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2,801 Answers

Are there any series whose convergence is unknown?

What is this series relating to the residues of the Gamma function?

Riemann hypothesis: is Bender-Brody-Müller Hamiltonian a new line of attack?

How was the integral for Zeta Function created

how to prove that $1^x+2^x+3^x+4^x+\cdots+N^x$ will never sum to a prime number except $1^x+2^x$?

On proving that $\sum\limits_{n=1}^\infty \frac{n^{13}}{e^{2\pi n}-1}=\frac 1{24}$

Why isn't the directional derivative generally scaled down to the unit vector?

The definition of "entire function"

Conjecture ${\large\int}_0^\infty\left[\frac1{x^4}-\frac1{2x^3}+\frac1{12\,x^2}-\frac1{\left(e^x-1\right)x^3}\right]dx=\frac{\zeta(3)}{8\pi^2}$

Is every Hilbert space separable?

Explicit value for series

Does the Mertens function have an infinite number of zeros?

$F(u) = F(u^2)$ if $u$ is algebraic of odd degree

Is an ideal finitely generated if its radical is finitely generated?

Why is proving the Riemann Hypothesis so hard?

Does a definite integral equal to the Möbius function exist?

Torus and Elliptic curves

Proving that $F(x)=\sum\limits_{k=1}^{p-1}\left(\frac{k}{p}\right)x^k$ has at least $\frac{p-1}{2}$ different complex roots

A probably wrong proof of the Riemann Hypothesis, but where is the mistake?

Infinite series involving Von Mangoldt's function

Does this sum of prime numbers converge?

Alternating series test for complex series

Relationship between GCD, LCM and the Riemann Zeta function

On the general form of the family $\sum_{n=1}^\infty \frac{n^{k}}{e^{2n\pi}-1} $

Is $\int\limits_0^\infty\frac{\sin y}{y^{s+1}}dy=-\Gamma(-s)\sin(\frac{\pi s}{2})$ for $\operatorname{Re}(s)\in (-1,0)$ obvious?

Unsolved problems in Fourier analysis

Euler Product formula for Riemann zeta function proof

Which derivatives are eventually periodic?

Zeta of 3, why cant we get the value the zeta of odd n?

$\lim_{n \to \infty}\frac{1}{n}\sum_{k = 1}^nf(k)$ where $f(n)$ is the largest prime factor exponent?