On Studying the Phase Behavior of the Riemann Zeta Function Along the\n Critical Line

2018/06/01 by Henrik Stenlund, Stenlund, Henrik
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics

paper · pdf · doi:10.48550/arxiv.1806.01148

Abstract

The critical line of the Riemann zeta function is studied from a new\nviewpoint. It is found that the ratio between the zeta function at any zero and\nthe corresponding one at a conjugate point has a certain phase and its absolute\nvalue is unity. This fact is valid along the whole critical line and only\nthere. The common functional equation is used with the aid of the function\nratio between any zero and its negative side pair, a complex conjugate. As a\nresult, an equation is obtained for solving the phase along the critical line.\n

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