A346289 Decimal expansion of the length of first, and largest, gap between nontrivial zeta zeros.

6, 8, 8, 7, 3, 1, 4, 4, 9, 7, 0, 3, 6, 8, 6, 1, 2, 0, 2, 1, 7, 1, 2, 2, 7, 6, 1, 0, 3, 3, 4, 4, 3, 2, 5, 0, 6, 5, 5, 0, 0, 8, 3, 4, 0, 9, 2, 0, 3, 5, 3, 8, 5, 7, 8, 9, 4, 3, 9, 5, 2, 9, 4, 3, 4, 3, 7, 6, 3, 5, 1, 5, 6, 2, 5, 9, 6, 3, 4, 0, 3, 4, 7, 6, 4, 6, 4

Offset: 1

Author

Charles R Greathouse IV, Jul 13 2021

Keywords

• nonn
• cons

Comments

Simonič shows that this gap is in fact larger than all other gaps between zeros of the Riemann zeta function, see the proof of Lemma 3.

Examples

			6.8873144970368612021712276103344325065500834092035385789439529434376351562596....
		

Links

• Aleksander Simonič, Lehmer pairs and derivatives of Hardy's Z-function, arXiv:1612.08627 [math.NT], 2016-2017.
• Index entries for zeta function.

Crossrefs

Cf. A065434, A058303.

Programs

Mathematica

Im[ZetaZero[2] - ZetaZero[1]] // RealDigits[#, 10, 88]& // First (* Peter Luschny, Jul 16 2021 *)

PARI

call((x,y)->y-x,lfunzeros(1,22))

Formula

Equals A065434 - A058303.