On q-orders in primitive modular groups

• Autorzy: Jacek Pomykała
• Języki publikacji: EN

Abstrakty

EN

We prove an upper bound for the number of primes p ≤ x in an arithmetic progression 1 (mod Q) that are exceptional in the sense that $ℤ*_p$ has no generator in the interval [1,B]. As a consequence we prove that if $Q > exp[c (log p)/(log B) (loglogp)]$ with a sufficiently large absolute constant c, then there exists a prime q dividing Q such that $ν_q(ord_p b) = ν_q(p-1)$ for some positive integer b ≤ B. Moreover we estimate the number of such q's under suitable conditions.

Kategorie tematyczne

• 11Z05: Miscellaneous applications of number theory
• 11M06: ζ ( s ) and L ( s , χ )
• 11M41: Other Dirichlet series and zeta functions
• 11R45: Density theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 166
• Numer: 4
• Strony: 397-404

Daty

wydano

2014

Twórcy

autor

Jacek Pomykała

• Institute of Mathematics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/aa166-4-5