Research: Number Theory

Riemann zeta Function ζ and its Derivative ζ

Riemann zeta Function $$\zeta$$ and its Derivative $$\zeta'$$

The absolute value of the Riemann zeta function ζ(σ+it) for 0σ8 and 0.1t60 over the complex plane. The white dots in the valleys are the non trivial zeros of the function. The Riemann hypothesis claims that the real part of all these zeros is 1/2.

Riemann zeta Function $$\zeta$$ and its Derivative $$\zeta'$$

The absolute value of the derivative ζ(σ+it) of the Riemann zeta function for 0σ8 and 0.1t60. The white dots in the valleys are zeros of the function. Both functions were plotted with the computer algebra system Sage.