Open Access
Translator Disclaimer
2010 Chebyshev's Bias for Products of Two Primes
Kevin Ford, Jason Sneed
Experiment. Math. 19(4): 385-398 (2010).


Under two assumptions, we determine the distribution of the difference between two functions each counting the numbers less than or equal to $x$ 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 analogues of similar results proved for primes in arithmetic progressions by Rubinstein and Sarnak.


Download Citation

Kevin Ford. Jason Sneed. "Chebyshev's Bias for Products of Two Primes." Experiment. Math. 19 (4) 385 - 398, 2010.


Published: 2010
First available in Project Euclid: 4 October 2011

zbMATH: 1280.11056
MathSciNet: MR2778652

Keywords: Chebyshev's bias , Prime number race

Rights: Copyright © 2010 A K Peters, Ltd.


Vol.19 • No. 4 • 2010
Back to Top