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Results tagged with analytic-number-theory
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user 136932
On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.
25
votes
Why is so much work done on numerical verification of the Riemann Hypothesis?
Part of the point is that such numerical checks can be demonstrations of the efficiency of this or that new algorithm. However, it is also the case that a finite check (that all the zeroes of $\zeta(s …
- 545
2
votes
0
answers
76
views
Accelerating convergence of a product by multiplying by zeta values: history?
Let $R(s_1,\dotsc,s_n) = \prod_p r(p^{-s_1},\dotsc,p^{-s_n})$, where
$r$ is a rational function on $n$ variables. Say we want to compute the value of $R(s_1,\dotsc,s_n)$ for some choice of $s_1,\dotsc …
- 545
1
vote
0
answers
126
views
How many solutions to $p_i|a_{i,1} p_1 + \dotsc + a_{i,n} p_n$?
Consider a system of $n$ divisibility conditions on $n$ prime variables:
$$p_i|a_{i,1} p_1 + \dotsc + a_{i,n} p_n,\;\;\;\;\;1\leq i\leq n,$$
where $a_{i,j}$ are bounded integers. How many solutions ar …
- 545