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Results tagged with analytic-number-theory
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user 74453
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.
3
votes
0
answers
157
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Liouville's function and Legendre Symbols
Suppose $p$ is a prime and let $\left(\frac{a}{p}\right)$ denote the Legendre symbol modulo $p$. If $a$ is not a perfect square, then one expects some cancellation in $\sum_{p<x}\left(\frac{a}{p}\righ …
- 671
3
votes
1
answer
434
views
Least prime for which a square-free integer is a non-residue
Suppose $a$ is a square-free integer and $\left(\frac{a}{p}\right)=1$ for the primes $p\leq k$. I'll call $a$ a quasi-square of order $k$. What I am interested in is the maximum value of $k$ in terms …
- 671
22
votes
1
answer
846
views
How big can a set of integers be if all pairs have small gcd?
Suppose $A\subset[1,N]$ is a set of integers. If for any distinct $a,b\in A$ we have $(a,b)\leq M$ then how big can $|A|$ be?
If $M=1$ then $|A|$ is at most $\pi(N)$ since the map $a\mapsto P_+(a)$ …
- 671
1
vote
1
answer
270
views
Least simultaneous quadratic non-residue
Suppose $p,q$ are distinct primes with least quadratic non-residues $n_p$ and $n_q$ respectively. Can one bound the least $n$ for which $\left(\frac{n}{p}\right)=\left(\frac{n}{q}\right)=-1$ in terms …
- 671