Variance of Distribution of Almost Primes in Arithmetic Progressions

C. R. Math. Rep. Acad. Sci. Canada Vol. 28, (1), 2006 pp. 12–16
(Received: 2006-01-20 )

Emmanuel Knafo, Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4; email: knafo@math.toronto.edu

Abstract/Résumé:

We give an effective lower bound for the variance of distribution of \(k\)-almost primes in arithmetic progressions. This lower bound approaches the expected asymptotic ‘exponentially fast’ as \(k\) goes to infinity.

Nous donnons une borne inférieure effective pour la variance de la distribution des nombres presque premiers d’ordre \(k\) dans les progressions arithmétiques. Cette borne inférieure s’approche de la valeur asymptotique attendue ‘exponentiellement vite’ quand \(k\) tend vers l’infini.

Keywords: almost primes, effective lower bound, generalized von Mangoldt function, truncated divisor sum

AMS Subject Classification: Distribution of integers with specified multiplicative constraints 11N25

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