It was not until 1859 that its namesake extended its domain to the whole complex plane, and since then much attention has been paid to the values it takes in the so-called "critical strip" of complex numbers whose real parts lie between zero and one.
Euler proved that the sum of the reciprocals of the prime numbers diverges by using his discovery that this function may be written as the product over all prime p of 1 over 1 minus p to the negative x. It was not until 1859 that its namesake extended its domain to the whole complex plane, and since then much attention has been paid to the values it takes in the so-called "critical strip" of complex numbers whose real parts lie between zero and one. FTP, name this function, defined as the sum as n goes from 1 to infinity of 1 over n to the z, which is the subject of the celebrated Riemann hypothesis.
Euler proved that the sum of the reciprocals of the prime numbers diverges by using his discovery that this function may be written as the product over all prime p of 1 over 1 minus p to the negative x.
Riemann zeta function