Fujii's development on Chebyshev's conjecture

Abstract

Chebyshev presented a conjecture after observing the apparent bias towards primes congruent to $3(\mathrm{mod}4)$. 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.