Fujii's development on Chebyshev's conjecture

2018/01/31 by Dave Platt, Tim Trudgian, Platt, Dave +1
Mathematics · #11M06 #11N13 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M06 #msc:11N13

paper · pdf · doi:10.48550/arxiv.1802.00089

arxiv created 2018/01/31 · arxiv updated 2018/02/02

Abstract

Chebyshev presented a conjecture after observing the apparent bias towards primes congruent to 3\pmod 4. His conjecture is equivalent to a version of the Generalised Riemann Hypothesis. Fujii strengthened this conjecture; we strengthen it still further using detailed computations of zeroes of Dirichlet L-functions.

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• Chebyshev's bias for Fermat curves of prime degree
• Chebyshev's bias without linear independence
• Chebyshev's Bias against Splitting and Principal Primes in Global Fields
• Unconditional Chebyshev biases in number fields
• On coefficients satisfying Chebyshev's approximation of π(x)