Numerical computations concerning Landau–Siegel zeros

Source abstract

We computationally verify that if L ( s , χ ) L(s,\chi ) is a quadratic Dirichlet L L -function modulo q ⩽ 10 10 q \leqslant 10^{10} then L ( σ , χ ) ≠ 0 L(\sigma ,\chi ) \neq 0 for real σ ⩾ 1 − 1 / ( 5 log ⁡ q ) \sigma \geqslant 1-1/(5\log q) . The number of verified moduli exceeds benchmarks due to Watkins (2004), Platt (2016), and Languasco (2023) by a factor between 66 66 and 25 25 ,000. Our new algorithm draws from zero-free region arguments.