Mathematics – Number Theory
Scientific paper
2011-12-06
Mathematics
Number Theory
19 pages
Scientific paper
For each nonprincipal Dirichlet character $\chi$, let $n_\chi$ be the least $n$ with $\chi(n) \notin \{0,1\}$. We show that as the average of $n_\chi$ over all nonprincipal characters $\chi$ modulo $q$ is $\ell(q) + o(1)$, where $\ell(q)$ denotes the least prime not dividing $q$. Moreover, if one averages over all nonprincipal characters of modulus at most $x$, the average approaches a particular limiting value 2.5350541804. We also prove a result of this type for cubic number fields: If one averages over all cubic fields $K$, ordered by the absolute value of their discriminant, then the mean value of the least rational prime that does not split completely in $K$ is another particular constant 2.1211027269.
Martin Greg
Pollack Paul
No associations
LandOfFree
The average least character nonresidue and further variations on a theme of Erdos does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The average least character nonresidue and further variations on a theme of Erdos, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The average least character nonresidue and further variations on a theme of Erdos will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-380376