2007/05/31 by Anthony Csizmazia, Csizmazia, Anthony
Mathematics · #11M06 #11M26 #11Mxx #30xx #42A82 #44A10 #60E10 #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:11M06 #msc:11M26 #msc:11Mxx #msc:30xx #msc:42A82 #msc:44A10 #msc:60E10
paper · pdf · doi:10.48550/arxiv.0705.4593
12 pages Added Part V to a contracted version of Part IV
arxiv created 2007/07/12 · arxiv updated 2009/12/01
In Part I an odd meromorphic function f(s) has been constructed from the Riemann zeta-function evaluated at one-half plus s. The conjunction of the Riemann hypothesis and hypotheses advanced by the author in Part I is assumed. In Part IV we derive the two-sided Laplace transform representation of f(s) on the open vertical strip V of all s with real part between zero and four. An additional hypothesis is used to prove that the Laplace density of f(s) on the strip V is positive. Let z(n) be the nth critical zero of the Riemann zeta-function of positive imaginary part in order of magnitude thereof. In Part V an expression is derived for z(1). A relation is obtained of the pair z(n) and the first derivative thereat of the zeta-function to the preceding such pairs.