A Brief note on the Riemann hypothesis

We deal with the Euler's alternating series of the Riemann zeta function to define a regularized ratio appeared in the functional equation even in the critical strip and show some evidence to indicate the hypothesis in this note.Comment: 4 pages; revised argument in Eq.(8), results unchange

N=2N=2 and 44 Super Yang-Mills Theories on M4×Z2×Z2M_4 \times Z_2 \times Z_2 Geometry

We derive the $N=2$ and $4$ super Yang-Mills theories from the viewpoint of the $M_4\times Z_2\times Z_2$ gauge theory. Scalars and pseudoscalars appearing in the theories are regarded as gauge fields along the directions on $Z_2\times Z_2$ discrete space.Comment: 13 pages, LaTeX fil