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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. $s=2$.)
Mar
1
comment Calculating an almost Gamma integral
Integrate term by term. You should recognize $\left(1-2^{1-x}\right)\zeta(x)$ as $\sum_n (-1)^{n+1}n^{-x}$.
Jan
18
answered Estimating the integrated Tchebychev function and calculating its error
Jan
13
revised Sum of Stieltjes constants
Added graphic and Mathematica code
Jan
11
answered Sum of Stieltjes constants
Jan
10
answered Inequality for Riemann zeta function
Jan
9
comment Sums of the negative integer powers of $\zeta$ zeros have an analytical expression…?
It's a plot of $\arg(\zeta(s))$, where the interval $[0,2\pi]$ is mapped to the color wheel. See my webpage.
Jan
8
answered Sums of the negative integer powers of $\zeta$ zeros have an analytical expression…?
Jan
8
revised Question about Riemann $\zeta(s)$ function zeroes
added the elementary proof of Titchmarsh.