2013/08/30 by Ross C. McPhedran, McPhedran, Ross C.
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #FOS: Physical sciences #Limits and Structures in Graph Theory #Mathematical Physics (math-ph) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1309.5845
openalex publication_date 2013/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper compares the distribution of zeros of the Riemann zeta function ζ(s) with those of a symmetric combination of zeta functions, denoted \cal T+(s), known to have all its zeros located on the critical line \Re(s)=1/2. Criteria are described for constructing a suitable quotient function of these, with properties advantageous for establishing an accessible proof that ζ(s) must also have all its zeros on the critical line: the celebrated Riemann hypothesis. While the argument put forward is not at the level of rigour required to constitute a full proof of the Riemann hypothesis, it should convince non-specialists that it must hold.