Special values of the Riemann zeta function capture all real numbers
Special values of the Riemann zeta function capture all real numbers
It is shown that the set of odd values \[ \{\zeta (3), \zeta (5),\dots , \zeta (2k+1),\dots \} \] of the Riemann zeta function is rich enough to capture real numbers in an approximation aspect. Precisely, we prove that any real number can be strongly approximated by certain linear combinations …