# Tagged Questions

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I'm interested in calculating all of the zeroes of the first derivative of the Riemann $\zeta$ function up to an arbitrary height. I know that (on the RH), all of these zeroes will have real part $\ge ... 1answer 273 views ### The geometric-mean factorial Think of the factorial as$f(n) = n \odot (n-1) \odot \cdots \odot 2 \odot 1$, where$\odot$is the binary operator for multiplication,$\cdot$. This suggests exploring replacing$\odot$with other ... 0answers 64 views ### Variational problem for optimal weight function leading to shorter intervals with many primes The motivation for the following problem stems from the recent preprint by James Maynard, see also Proposition 5 of the recent blogpost by Terrence Tao. The solution of this problem could give better ... 1answer 343 views ### Machin-like formulas for logarithms I found this math puzzle blog post http://fredrikj.net/blog/2013/03/machin-like-formulas-for-logarithms/ which I'm reposting here with permission. I'm setting this to community wiki to minimize the ... 0answers 420 views ### Parabolic cylinder functions - explicit estimates? I need estimates for the parabolic cylinder functions$U(a,z)$(first studied by Whittaker). Most work in the literature focuses on$a$real. As it happens, I am interested in$U(a,z)$on a strip in ... 1answer 256 views ### Repetitions of the totient In a program I'm writing I'm using that the function:$rphi(1) = 0rphi(n) = 1+rphi(phi(n))$grows very slowly. Judging from https://oeis.org/A003434 it would seam like it is approximately ... 1answer 341 views ### The complexity of the leading fractional bit of a power of a rational number On a mailing list (math-fun) that I subscribe to Dan Asimov asked what's the most efficient way to calculate the leading decimal digits (say 10 of them) of$(p/q)^n \bmod 1$where$p$and$q$are ... 1answer 324 views ### Calculating the constant in the Bateman-Horn-Stemmler conjecture Bateman & Horn [1], building on Bateman & Stemmler [2], give a conjectured formula for the density of numbers that produce simultaneous primes in a number of fixed polynomials. The constant ... 0answers 276 views ### Estimating a multinomial sum I have the following sum \sum_{r_1=q+1}^{\tau}\dots\sum_{r_\lambda=q+1}^{\tau}{\tau\choose r_1,\dots,r_\lambda,\tau-r_1-\dots -r_\lambda} (\Lambda-\lambda)^{\tau-r_1-\dots-r_\lambda} ... 2answers 795 views ### Calculating the infinite product from the Hardy-Littlewood Conjecture F The Hardy-Littlewood Conjecture F [1] involves the infinite product $$\prod\left(1-\frac{1}{\varpi-1}\left(\frac D\varpi\right)\right)$$ where$\varpi$ranges over the odd primes and$\left(\frac ...
Hi everyone I am trying the evaluate sums of the form $$\sum_{n_1>0,n_2>0,\ldots,n_m>0} \frac{1}{\big((a_{1,1}n_1 +\ldots +a_{1,m}n_m)^k \ldots (a_{m,1}n_1+ \ldots +a_{m,m}n_m)^k\big)}$$ ...