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math.NT2014
Counting solutions without zeros or repetitions of a linear congruence and rarefaction in b-multiplicative sequences
Alexandre Aksenov
Consider a strongly -multiplicative sequence and a prime . Studying its -rarefaction consists in characterizing the asymptotic behaviour of the sums of the first terms ind…
math.NT2011
Calculation of norms of some secial elements of cyclotomic fields
Alexandre Aksenov
In this article we prove that (1-zeta+zeta^2) is a unit in the ring of integers of the cyclotomic field where zeta is a primitive n-th root of unity and n is coprime to 2 and 3. We…
math.NT2011★ 1 cited
The Newman phenomenon and Lucas sequence
Alexandre Aksenov
This article gives an alternative proof of the fact that N_{Q(zeta)/Q}(1-zeta)=p where p is an odd prime number and zeta is a primitive p-th root of unity, and uses it to prove tha…