Chebyshev's Bias for Products of Two Primes

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.

• Type: Journal
• Year: 2010
• Where: EM
• Authors: Kevin Ford, Jason Sneed
• Keywords: Arithmetic Progression Modulo, Arithmetic Progressions, EM 2010, Extended Riemann Hypothesis, Management