2008/07/18 by Jerzy Cisło, Jerzy Cislo, Marek Wolf +2
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.0807.2971
Partly based on arXiv:math.NT/0607782, most of proofs changed, new figures. Some of the research results have been extracted and various new results added. New conjecture is formulated at the end
arxiv created 2008/07/18 · openalex publication_date 2008/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the relation between the Riesz and the Báez-Duarte criterion for the Riemann Hypothesis. In particular we present the relation between the function R(x) appearing in the Riesz criterion and the sequence ck appearing in the Báez-Duarte formulation. It is shown that R(x) can be expressed by ck, and, vice versa, the sequence ck can be obtained from the values of R(x) at integer arguments. Also, we give some relations involving ck and R(x), and value of the alternating sum of ck.