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Agno
  • Member for 13 years, 2 months
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1 vote
1 answer
167 views

Structural differences between closed forms of two related infinite products?

6 votes
1 answer
306 views

A conjectured series expression for the Riemann $\xi$-function and/or Completed L-series. Could this be proven?

0 votes
0 answers
74 views

Could the patterns in the roots of the Riemann-Liouville differintegral of $(s-1)\,L(s, \chi_{q,j})$ be explained?

0 votes
0 answers
48 views

A Riemann-Liouville differintegral for all entire Dirichlet L-series. Could it be simplified further?

3 votes
0 answers
228 views

Could the patterns in the roots of the Riemann-Liouville differintegral for $(s-1)\,\zeta(s)$ be explained?

5 votes
0 answers
357 views

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

2 votes
0 answers
157 views

How could this difference in series of power of zeros associated to counting integers and counting primes be explained?

4 votes
0 answers
222 views

To which value does this infinite sum of power series coefficients converge?

1 vote
1 answer
286 views

Continuing an analytic continuation of the Dirichlet $\eta$-function?

1 vote
1 answer
458 views

Deriving the functional equation for $\zeta(s)$ from summing the powers of the zeros required to count the integers

4 votes
1 answer
160 views

A Hadamard product representation for Keiper's $\tau$-function?

7 votes
0 answers
225 views

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

6 votes
3 answers
983 views

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

2 votes
0 answers
230 views

Could analytically deriving the next non-trivial zero of $\zeta(s)$ be made rigorous up to a fixed accuracy?

5 votes
0 answers
221 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?

18 votes
1 answer
674 views

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

5 votes
1 answer
306 views

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

2 votes
1 answer
189 views

Does this series, related to the Hasse/Ser series for $\zeta(s)$, converge for all $s \in \mathbb{C}$?

8 votes
1 answer
565 views

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

2 votes
0 answers
172 views

Are all complex zeros of $Li_s(z)\, \pm \, Li_{1-s}(z)$ on the critical line or outside the critical strip for $z \le -1$?

0 votes
1 answer
721 views

Is there information about the $\rho$'s hidden in the zeros of $\Re(\chi(s))$ ?

0 votes
0 answers
376 views

Does there exist a Weierstrass/Hadamard factorization for $\chi(s)-1$?

4 votes
0 answers
779 views

Wilson's theorem and the Zeta function

4 votes
4 answers
662 views

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

1 vote
3 answers
821 views

Possible locations for non trivial zeroes lying off the critical line

2 votes
0 answers
201 views

Are all zeros of $\dfrac{\Gamma'}{\Gamma^2}(s) \pm \dfrac{\Gamma'}{\Gamma^2}(1-s)$ either real or on the line with $\Re(s)=\frac12$?

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?

5 votes
1 answer
463 views

Viète's generalized infinite product yielding other converging values?

5 votes
2 answers
1k views

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

54 votes
6 answers
4k views

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