Variance of distribution of almost primes in arithmetic progressions
By: by Emmanuel Robert Knafo.
Published: 2006
Language: eng
Number of pages: 692
ISBN-13: 9780494158418
Description: In counting primes up to x in a given arithmetic progression, one resorts to the 'prime' counting function   yx;q,a= n&le;xn&equiv;a modq Ln  where &Lambda; is the usual von Mangoldt function. Analogously, to count those integers with no more than k prime factors, one can use   ykx;q,a =n&le;xn&equiv;a modq Lkn   where &Lambda;k is the generalized von Mangoldt function defined by &Lambda;k = mu * logk. Friedlander and Goldston gave a lower bound of the correct order of magnitude for the mean square sum   a modq a,q=1 yx;q,a -xfq 2   for q in the range   xlogx A  &le; q &le; x. Later, Hooley extended this range to   xexpclog x  &le; q &le; x. We obtain, in the larger range, a lower bound of the correct order of magnitude and approaching the expected asymptotic 'exponentially fast' as k approaches infinity.
Notes: Source: Dissertation Abstracts International, Volume: 67-06, Section: B, page: 3166.

Advisor: John Friedlander

Thesis (Ph.D.)--University of Toronto, 2006.

Includes bibliographic references.

Electronic version licensed for access by U. of T. users.