 Authors
 Year
 2001
 Title
 Chebyshev's bias for composite numbers with restricted prime divisors
 Publisher
 s.n.
 Document type
 Working paper
 Faculty
 Faculty of Science (FNWI)
 Institute
 Kortewegde Vries Institute for Mathematics (KdVI)
 Abstract

Let P(x,d,a) denote the number of primes p<=x with p=a(mod d). Chebyshev's bias is the phenomenon that `more often' P(x;d,n)>P(x;d,r), than the other way around, where n is a quadratic nonresidue mod d and r is a quadratic residue mod d. If P(x;d,n)>=P(x;d,r) for every x up to some large number, then one expects that N(x;d,n)>=N(x;d,r) for every x. Here N(x;d,a) denotes the number of integers n<=x such that every prime divisor p of n satisfies p=a(mod d). In this paper we develop some tools to deal with this type of problem and apply them to show that, for example, N(x;4,3)>=N(x;4,1) for every x.In the process we express the so called second order LandauRamanujan constant as an infinite series and show that the same type of formula holds true for a much larger class of constants.
 Permalink
 http://hdl.handle.net/11245/1.418832
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