User Agno

52 votes

6 answers

3k views

Are all zeros of $\Gamma(s) \pm \Gamma(1-s)$ on a line with real part = $\frac12$ ?

nt.number-theory gamma-function

asked Feb 23, 2012 at 19:46

23 votes

5 answers

2k views

Are the 'semi' trivial zeros of $\zeta(s) \pm \zeta(1-s)$ all on the critical line?

asked Feb 25, 2012 at 21:08

22 votes

2 answers

1k views

A closed form for an integral expressed as a finite series of $\zeta(2k+1)$, $\pi^m$ and a rational?

nt.number-theory integration riemann-zeta-function mathematical-software

asked May 20, 2017 at 16:18

18 votes

1 answer

628 views

Could computing the next prime in a finite Euler product be made rigorous?

nt.number-theory prime-numbers riemann-zeta-function euler-product

asked Jul 10, 2020 at 16:37

17 votes

3 answers

2k views

Does this infinite sum provide a new analytic continuation for $\zeta(s)$?

nt.number-theory riemann-zeta-function riemann-hypothesis

asked Aug 23, 2013 at 23:48

9 votes

0 answers

448 views

Do all complex zeros in the strip of $\frac{\zeta(s)}{\Gamma(s)} - \frac{\Gamma(1-s)}{\zeta(1-s)}$ lie on the critical line?

nt.number-theory riemann-zeta-function riemann-hypothesis gamma-function

asked Jan 18, 2015 at 18:24

9 votes

1 answer

390 views

Do the complex zeros of the sum/difference of these series all reside on the line $\Re(s)=\frac12$?

nt.number-theory sequences-and-series

asked Oct 4, 2015 at 15:31

8 votes

1 answer

517 views

Why was the factor $\frac12$ introduced in the Riemann $\xi$ function?

nt.number-theory reference-request ho.history-overview riemann-zeta-function

asked Dec 11, 2019 at 23:52

7 votes

0 answers

215 views

Is there a connection between the sequence of a finite number of Stieltjes constants and the integer partitions number?

nt.number-theory sequences-and-series riemann-zeta-function partitions

asked Oct 22, 2020 at 15:40

7 votes

0 answers

182 views

How to assess the influence of a specific term in this telescoping series for $\zeta(s)$?

nt.number-theory sequences-and-series riemann-zeta-function riemann-hypothesis

asked Mar 14, 2015 at 15:42

7 votes

1 answer

659 views

Are all complex zeros of $\zeta(s) \pm \zeta(-s)$ on the line with $\Re(s)=0$?

nt.number-theory riemann-zeta-function

asked Jan 25, 2014 at 21:56

7 votes

3 answers

1k views

Values where infinite products of primes and composites are equal

nt.number-theory prime-numbers

asked Jan 25, 2011 at 19:22

6 votes

0 answers

1k views

Are all complex zeros of $\frac{\Gamma(s)}{z}Li_s(z) \, \pm \, \frac{\Gamma(1-s)}{z}Li_{1-s}(z)$ on the critical line for all $z \lt 1$?

nt.number-theory riemann-zeta-function riemann-hypothesis

asked Jul 27, 2014 at 18:17

6 votes

1 answer

611 views

Is there a connection between the closed forms of these two infinite products?

nt.number-theory riemann-zeta-function riemann-hypothesis

asked Feb 21, 2013 at 23:35

6 votes

3 answers

947 views

Does this 'alternating' Euler product converge for all $\Re(s) > 0$?

nt.number-theory prime-numbers sequences-and-series euler-product

asked Mar 6, 2014 at 13:58

6 votes

1 answer

497 views

Are all complex zeros of $\dfrac{\zeta'}{\zeta}(s) \pm \dfrac{\zeta'}{\zeta}(1-s)$ on the critical line $\Re(s)=\frac12$?

nt.number-theory riemann-zeta-function

asked May 10, 2015 at 10:51

6 votes

2 answers

374 views

Does the limit of this product over primes converge for all $\Re(s) > \frac12$?

nt.number-theory prime-numbers limits-and-convergence products euler-product

asked Nov 29, 2015 at 11:30

5 votes

0 answers

206 views

Are the ordinates of the non-trivial zeros of $\zeta(s)$ uniformly distributed around the mid points of Gram point intervals they can be mapped to?

nt.number-theory riemann-zeta-function gaussian rootfinding

asked Jul 21, 2020 at 22:28

5 votes

1 answer

269 views

Three integral expressions for integer values of $\zeta(s)$. Could these be further reduced to known integrals?

nt.number-theory integration riemann-zeta-function

asked Jun 21, 2020 at 18:09

5 votes

0 answers

282 views

Are there infinitely many zeros of $\chi(s)+ \dfrac{2^{s}- 2^{2s-1}}{2^{s}-1}$ on the critical line?

nt.number-theory prime-numbers riemann-zeta-function riemann-hypothesis

asked Jun 11, 2015 at 22:42

5 votes

1 answer

796 views

Does the Euler product for $L(s,\chi_4)$ also converge in the right half of the critical strip?

nt.number-theory prime-numbers analytic-number-theory dirichlet-series euler-product

asked Jun 17, 2015 at 21:07

5 votes

0 answers

274 views

Telescoping series for $\zeta(s)$, question about the basic ideas and a specific series

nt.number-theory sequences-and-series riemann-zeta-function

asked Jan 4, 2015 at 16:49

5 votes

0 answers

379 views

A relation between the Gamma function and the Mobius function?

nt.number-theory riemann-zeta-function gamma-function

asked Jan 16, 2015 at 23:38

5 votes

1 answer

554 views

Can $\zeta(s)$ for $\Re(s)>1$ be split into two factors that each can be analytically continued?

nt.number-theory riemann-zeta-function

asked Jun 23, 2013 at 15:46

5 votes

1 answer

460 views

Viète's generalized infinite product yielding other converging values?

nt.number-theory cv.complex-variables

asked Dec 3, 2011 at 15:11

5 votes

3 answers

722 views

A closed form of infinite products of complex zeros involving $\Im(\rho_n)$. Does a proof of this closed form imply RH?

nt.number-theory riemann-zeta-function riemann-hypothesis

asked Jan 2, 2013 at 15:32

5 votes

2 answers

1k views

The distribution of balls in a Bean Machine that omits all the "prime pegs"?

nt.number-theory probability-distributions

asked Feb 14, 2013 at 22:10

4 votes

0 answers

766 views

Wilson's theorem and the Zeta function

nt.number-theory riemann-zeta-function

asked Aug 6, 2011 at 18:16

4 votes

4 answers

643 views

What happens to $\zeta(s)$ when all its $\Im(\rho_n)$ are "scaled" linearly?

nt.number-theory riemann-zeta-function riemann-hypothesis

asked Dec 2, 2012 at 0:32

4 votes

1 answer

665 views

A Hadamard product of the zeros of the Riemann integral. Does it put any constraints on where the $\rho$'s can reside in the critical strip?

nt.number-theory riemann-zeta-function riemann-hypothesis hadamard-product

asked May 10, 2014 at 20:22

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73 Questions

Are all zeros of $\Gamma(s) \pm \Gamma(1-s)$ on a line with real part = $\frac12$ ?

Are the 'semi' trivial zeros of $\zeta(s) \pm \zeta(1-s)$ all on the critical line?

A closed form for an integral expressed as a finite series of $\zeta(2k+1)$, $\pi^m$ and a rational?

Could computing the next prime in a finite Euler product be made rigorous?

Does this infinite sum provide a new analytic continuation for $\zeta(s)$?

Do all complex zeros in the strip of $\frac{\zeta(s)}{\Gamma(s)} - \frac{\Gamma(1-s)}{\zeta(1-s)}$ lie on the critical line?

Do the complex zeros of the sum/difference of these series all reside on the line $\Re(s)=\frac12$?

Why was the factor $\frac12$ introduced in the Riemann $\xi$ function?

Is there a connection between the sequence of a finite number of Stieltjes constants and the integer partitions number?

How to assess the influence of a specific term in this telescoping series for $\zeta(s)$?

Are all complex zeros of $\zeta(s) \pm \zeta(-s)$ on the line with $\Re(s)=0$?

Values where infinite products of primes and composites are equal

Are all complex zeros of $\frac{\Gamma(s)}{z}Li_s(z) \, \pm \, \frac{\Gamma(1-s)}{z}Li_{1-s}(z)$ on the critical line for all $z \lt 1$?

Is there a connection between the closed forms of these two infinite products?

Does this 'alternating' Euler product converge for all $\Re(s) > 0$?

Are all complex zeros of $\dfrac{\zeta'}{\zeta}(s) \pm \dfrac{\zeta'}{\zeta}(1-s)$ on the critical line $\Re(s)=\frac12$?

Does the limit of this product over primes converge for all $\Re(s) > \frac12$?

Are the ordinates of the non-trivial zeros of $\zeta(s)$ uniformly distributed around the mid points of Gram point intervals they can be mapped to?

Three integral expressions for integer values of $\zeta(s)$. Could these be further reduced to known integrals?

Are there infinitely many zeros of $\chi(s)+ \dfrac{2^{s}- 2^{2s-1}}{2^{s}-1}$ on the critical line?

Does the Euler product for $L(s,\chi_4)$ also converge in the right half of the critical strip?

Telescoping series for $\zeta(s)$, question about the basic ideas and a specific series

A relation between the Gamma function and the Mobius function?

Can $\zeta(s)$ for $\Re(s)>1$ be split into two factors that each can be analytically continued?

Viète's generalized infinite product yielding other converging values?

A closed form of infinite products of complex zeros involving $\Im(\rho_n)$. Does a proof of this closed form imply RH?

The distribution of balls in a Bean Machine that omits all the "prime pegs"?

Wilson's theorem and the Zeta function

What happens to $\zeta(s)$ when all its $\Im(\rho_n)$ are "scaled" linearly?

A Hadamard product of the zeros of the Riemann integral. Does it put any constraints on where the $\rho$'s can reside in the critical strip?