Investigation about a statement equivalent to Riemann Hypothesis (RH) applied to Dirichlet primitive L functions

Abstract

We try to apply a known equivalence, for RH about Riemann Z function, to Dirichlet L functions with primitive characters. A key point is the study of positivity condition in phase derivative of primitive L functions. In order to write it in workable form it is crucial to extend Euler product to critical strip. By exploiting the concept of y-friable integers this task is accomplished. Afterward, by use of the ratio limit in P.N.T.,it is shown that this partial derivative expression cannot be negative along critical line. Fulfilling so the statement above. Then, if the mentioned equivalence is true, this implies that no off-critical line zeros are allowed for at least odd-primitive Dirichlet L functions.

arXiv comment46 pages, 20 figures