Chebyshev's bias for products of two primes

Kevin Ford, Jason Sneed

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)385-398
Number of pages14
JournalExperimental Mathematics
Issue number4
StatePublished - 2010


  • Chebyshev's bias
  • Prime number race

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Chebyshev's bias for products of two primes'. Together they form a unique fingerprint.

Cite this