A072080 Number of (nontrivial) zeros of zeta(z) with 0 < Im(z) < 10^n.

0, 29, 649, 10142, 138069, 1747146, 21136125, 248008025, 2846548032, 32130158315, 357948363084, 3945951430271, 43124192297102, 467888702914983, 5045354828589535, 54118226280292478

Offset: 1

Author

Eric W. Weisstein, Jun 13 2002

Keywords

• nonn
• more

Comments

a(n) ~ A259506(10^n). - Arkadiusz Wesolowski, Nov 08 2015

Links

• LMFDB base, Zeros of zeta(s) (computed by David Platt).
• Andrew Odlyzko, Tables of zeros of the Riemann zeta function
• Mathematics StackExchange user Rudolph, Does this contour integral actually count the roots of zeta(s) with imaginary part , 2018. [Gives a(17)-a(20) as 577829042746896155, 6144758226908675407, 65112260263483892774, 687769382578810314775.]
• Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros
• Eric Weisstein's World of Mathematics, Xi-Function
• Index entries for zeta function.

Programs

PARI

a(n)=#lfunzeros(lzeta,10^n) \\ Charles R Greathouse IV, Mar 10 2016

Extensions

More terms from Andrew Odlyzko, Jun 14 2002

a(7)-a(11) based on LMFDB data from Artur Jasinski, Jan 03 2020

a(11) corrected based on LMFDB data by Charles R Greathouse IV, Aug 23 2022

a(12)-a(16) added by Fredrik Johansson, May 01 2023