zetafunktsioonile
Zetafunktsioonile, also known as the Riemann zeta function, is a fundamental concept in mathematics, named after the German mathematician Bernhard Riemann. It is defined for complex numbers with a real part greater than 1 as the infinite series:
ζ(s) = ∑ from n=1 to ∞ of 1/n^s
where s is a complex number. The zeta function plays a crucial role in analytic number theory,
The Riemann zeta function satisfies several important functional equations. One of the most famous is:
ζ(s) = 2^s * π^(s-1) * sin(πs/2) * Γ(1-s) * ζ(1-s)
where Γ is the Gamma function. This equation relates the values of the zeta function on the line
The Riemann hypothesis is a conjecture that all non-trivial zeros of the zeta function have a real