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Of central importance in number theory is the distribution of the complex zeros of f(s), all of which are in the critical strip 0 < a < 1 and are symmetrically located about the real axis and about the critical line a = 1/2. Riemann conjectured in 1859 that all of these zeros are on the critical line; this conjecture, which is still unproved, is known as the Riemann Hypothesis. The number of zeros of Ç(s) in the region 0 < t < T of the critical strip is denoted N(T) and is given asymptotically by

At least two fifths of the zeros of the Riemann zeta function are on the critical line