Chebyshev's bias for products of two primes

Details Chebyshev's bias for products of two primes Chebyshev's bias for products of two primes

2009-08-03

arxiv.org/abs/0908.0093v2

Mathematics

Number Theory

v2. 18 pages. To appear in Exper. Math. Tiny changes/corrections

Scientific paper

Under two assumptions, we determine the distribution of the difference between two functions each counting the numbers < x that are in a given arithmetic progression modulo q and the product of two primes. The two assumptions are (i) the Extended Riemann Hypothesis for Dirichlet L-functions modulo q, and (ii) that the imaginary parts of the nontrivial zeros of these L-functions are linearly independent over the rationals. Our results are analogs of similar results proved for primes in arithmetic progressions by Rubinstein and Sarnak. In particular, we show that the bias for products of two primes is always reversed from the bias for primes. For example, while Rubinstein and Sarnak showed, under (i) and (ii), that 99.6% of the time there are more primes up to x which are 3 mod 4 than those which are 1 mod 4, we show that 89.4% of the time, there are more products of two primes which are 1 mod 4 than 3 mod 4.

Affiliated with

Also associated with

No associations

Rating

Chebyshev's bias for products of two primes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Chebyshev's bias for products of two primes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Chebyshev's bias for products of two primes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-453061