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Agno
  • Member for 11 years, 6 months
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52 votes
6 answers
3k views

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

23 votes
5 answers
2k views

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

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?

18 votes
1 answer
628 views

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

17 votes
3 answers
2k views

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

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?

9 votes
1 answer
390 views

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

8 votes
1 answer
517 views

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

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?

7 votes
0 answers
182 views

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

7 votes
1 answer
659 views

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

7 votes
3 answers
1k views

Values where infinite products of primes and composites are equal

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 $z \lt 1$?

6 votes
1 answer
611 views

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

6 votes
3 answers
947 views

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

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 $\Re(s)=\frac12$?

6 votes
2 answers
374 views

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

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?

5 votes
1 answer
269 views

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

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?

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?

5 votes
0 answers
274 views

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

5 votes
0 answers
379 views

A relation between the Gamma function and the Mobius function?

5 votes
1 answer
554 views

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

5 votes
1 answer
460 views

Viète's generalized infinite product yielding other converging values?

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?

5 votes
2 answers
1k views

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

4 votes
0 answers
766 views

Wilson's theorem and the Zeta function

4 votes
4 answers
643 views

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

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?