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An arithmetic function

K. Nageswara Rao (1971)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Average r-rank Artin conjecture

Lorenzo Menici, Cihan Pehlivan (2016)

Acta Arithmetica

Let Γ ⊂ ℚ * be a finitely generated subgroup and let p be a prime such that the reduction group Γₚ is a well defined subgroup of the multiplicative group ₚ*. We prove an asymptotic formula for the average of the number of primes p ≤ x for which [ₚ*:Γₚ] = m. The average is taken over all finitely generated subgroups Γ = a , . . . , a r * , with a i and a i T i , with a range of uniformity T i > e x p ( 4 ( l o g x l o g l o g x ) 1 / 2 ) for every i = 1,...,r. We also prove an asymptotic formula for the mean square of the error terms in the asymptotic formula with a similar...

Distribution of quadratic non-residues which are not primitive roots

S. Gun, B. Ramakrishnan, Binod Kumar Sahoo, Ravindranathan Thangadurai (2005)

Mathematica Bohemica

In this article we study, using elementary and combinatorial methods, the distribution of quadratic non-residues which are not primitive roots modulo p h or 2 p h for an odd prime p and h 1 an integer.

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