Geodesic
On $q$-orders in primitive modular groups
Jacek Pomykała1
1 Institute of Mathematics Faculty of Mathematics, Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland
Acta Arithmetica, Tome 166 (2014) no. 4, pp. 397-404

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove an upper bound for the number of primes $p \leq x$ in an arithmetic progression $1 \pmod Q$ that are exceptional in the sense that $\mathbb{Z}^*_p$ has no generator in the interval $[1, B].$ As a consequence we prove that if $Q >\exp \bigl[c\frac{\log p}{\log B} (\log \log p)\big]$ with a sufficiently large absolute constant $c$, then there exists a prime $q$ dividing $Q$ such that $\nu_q(\mathop{\rm ord}_p b) =\nu_q(p-1)$ for some positive integer $b\le B.$ Moreover we estimate the number of such $q$'s under suitable conditions.
DOI : 10.4064/aa166-4-5
Keywords: prove upper bound number primes leq arithmetic progression pmod exceptional sense mathbb * has generator interval consequence prove exp bigl frac log log log log sufficiently large absolute constant there exists prime dividing mathop ord p positive integer moreover estimate number under suitable conditions

Jacek Pomykała 1

1 Institute of Mathematics Faculty of Mathematics, Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland 
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Jacek Pomykała. On $q$-orders in primitive modular groups. Acta Arithmetica, Tome 166 (2014) no. 4, pp. 397-404. doi: 10.4064/aa166-4-5

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