A Wiener-Ikehara type theorem and its application to Chebyshev bounds for Beurling primes

Yarne Tranoy, Jasson Vindas

We provide a new version of the Wiener-Ikehara theorem where one deduces bounds $$0<\underset{x\to \infty }{\mathrm{liminf}}\frac{S(x)}{e^x}\le \underset{x\to \infty }{\mathrm{limsup}}\frac{S(x)}{e^x}<\infty$$…