User Agno

23

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

Aug 8 '17 at 1:16 jeq 1,220

10

23

votes

5

answers

2k

views

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

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

Mar 5 '16 at 23:24 Community♦ 1

4

21

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

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3

18

votes

1

answer

523

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

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

Jul 12 at 15:38 Andreas Weingartner 905

2

16

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

Aug 29 '13 at 22:00 Community♦ 1

4

9

votes

0

answers

431

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

Jan 31 '15 at 0:18 Agno 3,653

1

8

votes

1

answer

379

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

Oct 10 '15 at 10:35 Agno 3,653

7

votes

1

answer

435

views

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

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

Dec 12 at 4:00 Lior Silberman 2,303

4

7

votes

0

answers

176

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

Mar 14 '15 at 15:42 Community♦ 1

2

7

votes

3

answers

1k

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Values where infinite products of primes and composites are equal

nt.number-theory prime-numbers

May 18 '13 at 22:22 Community♦ 1

1

6

votes

2

answers

357

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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

Nov 29 '15 at 20:43 Igor Rivin 91.3k

6

votes

1

answer

412

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

May 10 '15 at 15:39 Peter Michor 23.3k

2

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

Aug 3 '14 at 12:58 Community♦ 1

6

votes

1

answer

616

views

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nt.number-theory riemann-zeta-function

Feb 7 '14 at 22:54 Community♦ 1

3

6

votes

1

answer

586

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

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

Mar 12 '13 at 15:41 Agno 3,653

5

votes

1

answer

208

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

nt.number-theory integration riemann-zeta-function

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5

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1

answer

454

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Viète's generalized infinite product yielding other converging values?

nt.number-theory cv.complex-variables

Oct 18 '17 at 14:19 jeq 1,220

2

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

Oct 16 '17 at 8:16 Aaron Meyerowitz 27.3k

5

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1

answer

518

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

May 13 '17 at 6:00 Martin Sleziak 4,102

5

votes

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269

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Jun 12 '15 at 14:04 Community♦ 1

2

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0

answers

340

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

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5

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258

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

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

Jan 4 '15 at 16:49 Community♦ 1

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5

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3

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691

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Jul 26 '13 at 19:52 Community♦ 1

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4

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Wilson's theorem and the Zeta function

nt.number-theory riemann-zeta-function

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4

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613

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

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

Feb 26 '18 at 1:04 jeq 1,220

4

votes

1

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263

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Another integral that has a closed form involving finite series of $\zeta(2k+1)$'s. Could it be reflexive?

nt.number-theory integration riemann-zeta-function integer-sequences

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

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1

4

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1

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464

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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

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612

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

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

Jul 24 at 13:55 Agno 3,653

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66 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?

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

Values where infinite products of primes and composites are equal

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

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

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 $z \lt 1$?

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

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

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

Viète's generalized infinite product yielding other converging values?

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

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

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

A relation between the Gamma function and the Mobius function?

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

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

Wilson's theorem and the Zeta function

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

Another integral that has a closed form involving finite series of $\zeta(2k+1)$'s. Could it be reflexive?

Do the roots of this equation involving two Euler products all reside on the critical line?

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?

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

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