A231165 Number of Gram blocks [g(j), g(j+1)) up to 10^n, 0 <= j < 10^n, which contain exactly three zeros of Z(t), where Z(t) is the Riemann-Siegel Z-function.

0, 6, 86, 1289, 14932, 166570

Offset: 3

Author

Arkadiusz Wesolowski, Nov 04 2013

Keywords

• nonn
• more

Comments

We call a Gram point g(j) "good" if j is not in A114856, and "bad" otherwise. A "Gram block of length k" is an interval [g(j), g(j+k)) such that g(j) and g(j+k) are good Gram points, g(j+1), ..., g(j+k-1) are bad Gram points, and k >= 1.

Links

• Richard P. Brent, On the Zeros of the Riemann Zeta Function in the Critical Strip, Math. Comp. 33 (1979), pp. 1361-1372.
• Eric Weisstein's World of Mathematics, Gram Block
• Eric Weisstein's World of Mathematics, Gram Point
• Eric Weisstein's World of Mathematics, Riemann-Siegel Functions

Crossrefs

Cf. A114856, A231157-A231164.