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Results tagged with computational-number-theory
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user 37555
Computational Number Theory is for explicit calculations or algorithms involving anything of interest to number theorists.
1
vote
Spreading-out integers via multiplication
Choosing $N$ at random and checking should work. Put $e(t)=e^{2\pi i t/m}$. Then we have
\begin{eqnarray*}
\sum_{N=1}^m\sum_{k=1}^K\left|\sum_{i=1}^ne(k N a_i)\right|^2 & = &
\sum_{N=1}^m\sum_{k=1}^K\ …
5
votes
Accepted
Specializing non-trivial primality tests
Checking whether an integer $n$ has a divisor in a given interval is essentially equivalent to factorization. Factoring is essentially equivalent to finding the smallest prime factor. So suppose that …
5
votes
Analogues of the Riemann zeta function that are more computationally tractable?
Let $p_k$ be the $k$-th prime number, and pick a sequence of primes $q_k$, such that $q_k\sim p_k^{3/2}$. Let $G$ be the arithmetic semigroup consisting of all integers not divisible by one of the $q_ …