Unconditional construction of moduli sequences forces generalized Skewes numbers to grow rapidly in quadratic-residue races, disproving Fiorilli's conjecture, with conditional upper bounds under GRH and effective linear independence via quantitative Wasserstein convergence rates.
Wintner,On the Asymptotic Distribution of the Remainder Term of the Prime-Number Theorem, Amer
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A Wasserstein metric approach to generalized Skewes' numbers. I. Prime number races
Unconditional construction of moduli sequences forces generalized Skewes numbers to grow rapidly in quadratic-residue races, disproving Fiorilli's conjecture, with conditional upper bounds under GRH and effective linear independence via quantitative Wasserstein convergence rates.