Some high peaks of partial Euler Product of the lowest primes on the Riemann Zeta critical line, in the interval (10^20 < T < 10^400 ) providing a proxy lower bound on Riemann Zeta function growth

John Martin
2018 Figshare  
Using pari/gp software and the Lenstra-Lenstra-Lovász (LLL) basis reduction algorithm, repeated grid searches using larger and larger sets of the irrationals log(2 ∗ N_1 )/2π (150-850 elements) have produced many positions on the Riemann Zeta critical line (10^20 < T < 10^400 ), that correspond to large partial Euler product peaks using only the lowest primes (n=1000). In comparison to the known behaviour for large peaks of the Riemann Zeta function (17 < T < 10^32 ), the partial Euler product
more » ... eaks appear to be proxy lower bounds of the |ζ(1/2 + iT )| growth rate. Several partial Euler product peaks exceed heights of 1,000,000 for T > 10^300 .
doi:10.6084/m9.figshare.7185092.v2 fatcat:dmxqdthllbbphlxjmp3ty6dv6y