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Oct
17
comment zero distribution of the Fourier kernel $\Phi(u)$ for Riemann $\Xi(z)$ function
Yes. $\ \ \ \ \ $
Oct
17
answered zero distribution of the Fourier kernel $\Phi(u)$ for Riemann $\Xi(z)$ function
Sep
19
answered Does the series $\sum_{n=1}^\infty (-1)^n \frac{\cos(\ln(n))}{n^{\epsilon}},\,\epsilon>0$ converge?
Sep
10
revised Asymptotics for zeta zeros?
added improved asymptotic.
Sep
8
awarded  Yearling
Sep
7
answered Asymptotics for zeta zeros?
Sep
5
comment Riemann Zeta Function On Line Re(s)=1
The geometric series is the answer to quite a lot of questions.
Sep
4
answered Riemann Zeta Function On Line Re(s)=1
May
29
awarded  Organizer
May
29
revised Diophantine equation: $2 a^2 + 2 b^2 = c^2 + d^2$
more appropriate tags
May
29
suggested suggested edit on Diophantine equation: $2 a^2 + 2 b^2 = c^2 + d^2$
May
29
comment Analytic continuation of Zeta type function
In fact, $\Omega(k)$ is not the number of distinct prime factors of $k$; it is the total number of prime factors. E.g., $\Omega(9)=2$. With this adjustment, the OP's identity is correct, as is the answer below. BTW, $(-1)^{\Omega(k)}$ is called Liouville's function, denoted $\lambda(k)$.
Apr
28
revised What's the generalisation of the quotient rule for higher derivatives?
Added parentheses to indicate derivative (v. exponent)
Apr
28
suggested suggested edit on What's the generalisation of the quotient rule for higher derivatives?
Apr
23
answered $\zeta(2 + it) = \zeta(2-it)$
Mar
21
awarded  Self-Learner
Jan
11
awarded  Critic
Sep
8
awarded  Yearling
Jun
25
comment Proof of a Dirichlet's theorem using the Riemann zeta function?
Which Theorem in Davenport proves Dirichlet's Theorem on primes in progressions using ONLY the Riemann zeta function? Specific citation please, because I'm unaware of such a proof.
Mar
8
comment Can the Basel problem be solved by Leibniz today?
It would be quite surprising if you could prove, or even give a heuristic argument, for (1) => (2). They are values of two different $L$-functions (namely $\zeta(s)$ and $L(s,\chi)$ for the nontrivial character modulo $4$) at two different values of $s$ ($s=1$ v. $s=2$.)