2023/03/12 by Zhang, Ruiming
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2303.09396
In this work we apply Hausdorff moment problem to prove a necessary and sufficient condition for a complex sequence to be positive. Then we apply it to a subclass of genus 0 entire functions f(z) to obtain an infinite family of necessary and sufficient conditions for f(z) to have only negative roots, which in turn to give infinite many necessary and sufficient conditions for the Riemann hypothesis and the generalized Riemann hypothesis with a primitive Dirichlet character.