Self-similarity along the line Re(L(χ, s)) = 1 for 1st degree L functions near (i) large peaks and (ii) points known to correspond to large Riemann Zeta function peaks

John Martin
Two types of self-similarity exhibited in 1st degree L-functions on the line S=1+i*T are examined in therange (10 5 < T < 10 30 ). Firstly, it is observed that there is extended mesoscale structure surrounding thelarge peaks of the L-function on the line S=1+i*T reflecting closely the product function of (i) a truncatedRiemann Zeta function near the real axis with (ii) simple Euler factor type terms arising from the absentlower modulo primes of the L-function. A second self-similarity pattern
more » ... micking a version of the L-functionnear the real axis (S=1) occurs around points known to correspond to large Riemann Zeta function peaks.Following previous work, simple expressions are provided to approximate the known lower bound height andlocal structure of the self-similarity features about large 1st degree L-function peaks for σ ≥ 1.
doi:10.6084/m9.figshare.13242101.v4 fatcat:3os6sakeofefxppnmwvzatg76a