180 citations · 357 across the 58 of their papers we have counts for
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Chebyshev's conjecture and the prime number race
Kevin Ford, Sergei Konyagin
We survey results about prime number races, that is, results about the relative sizes of prime counting functions , with fixed and varying. In particular, we de…
The prime number race and zeros of Dirichlet L-functions off the critical line, II
Kevin Ford, Sergei Konyagin
We continue our examination the effects of certain hypothetical configurations of zeros of Dirichlet -functions lying off the critical line ("barriers") on the relative magnitud…
The prime number race and zeros of Dirichlet L-functions off the critical line
Kevin Ford, Sergei Konyagin
Let denote the number of primes in the progression modulo . We study subtle inequities in these functions, with fixed and variable (sometimes ca…
On two conjectures of Sierpiński concerning the arithmetic functions and
Kevin Ford, Sergei Konyagin
Let denote the sum of the positive divisors of . We prove that for any positive integer , there is a number for which the equation has exactly solutio…
Vinogradov's integral and bounds for the Riemann zeta function
Kevin Ford
We show for all and that , where is the Riemann zeta function. This significantly improves the previous bounds…
Zero-free regions for the Riemann zeta function
Kevin Ford
We improve existing explicit bounds of Vinogradov-Korobov type for zero-free regions of the Riemann zeta function, both for large height t and for every t. A primary input is an ex…