A variance for k-free numbers in arithmetic progressions

• Autores: R. C. Vaughan
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 91, Nº 3, 2005, págs. 573-597
• Idioma: inglés
• DOI: 10.1112/s0024611505015352
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• Resumen

  • The second moment for the the distribution of $k$-free numbers into arithmetic progression is studied and the asymptotic formula of Hooley-Montgomery type is obtained for a wider range of values for the modulus than hitherto. In the special case of squarefree numbers this improves on the theorem of Warlimont from 1980.