Rosser's Rule

Rosser's rule states that every Gram block contains the expected number of roots, which appears to be true for computable Gram blocks. Rosser et al. (1969) expressed a belief that this phenomenon will not continue, and the fact that it in fact fails infinitely often was subsequently proved by Lehman (1970).

REFERENCES:

Edwards, H. M. Riemann's Zeta Function. New York: Dover, 2001.

Lehman, R. S. "On the Distribution of Zeros of the Riemann Zeta Function." Proc. London Math. Soc. 20, 303-320, 1970.

Rosser, J. B.; Yohe, J. B.; and Schoenfeld, L. "Rigorous Computation and the Zeros of the Riemann Zeta-Function." In Cong. Proc. Int. Fed. Information Process., 1968. Washington, DC: Spartan, pp. 70-76, 1969.