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On q-orders in primitive modular groups

Jacek Pomykała (2014)

Acta Arithmetica

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 * p has no generator in the interval [1,B]. As a consequence we prove that if Q > e x p [ c ( l o g p ) / ( l o g B ) ( l o g l o g p ) ] with a sufficiently large absolute constant c, then there exists a prime q dividing Q such that ν q ( o r d p b ) = ν q ( p - 1 ) for some positive integer b ≤ B. Moreover we estimate the number of such q’s under suitable conditions.

On the distribution of integral and prime divisors with equal norms

Baruch Z. Moroz (1984)

Annales de l'institut Fourier

In finite Galois extensions k 1 , ... , k r of Q with pairwise coprime discriminants the integral and the prime divisors subject to the condition N k 1 / Q 𝔞 r = = N k r / Q 𝔞 r are equidistributed in the sense of E. Hecke.

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