OFFSET
-1,8
COMMENTS
"The zeta function is zero at every negative even number (the trivial zeros) and the successive peaks and troughs now ... get rapidly more and more dramatic as you head west (negative). The last trough I show, which occurs at s = -49.587622654 [6410765611566721701427687663932953145937293907205304283197148592994576700093701122213865946359936710563061421]..., has a depth of about 305,507,128,402,512,981,000,000 (305507128402512978943383.678283221037793184376280971034994413486029678612346873189963110344084662196600996131417814311). You see the difficulty of graphing the zeta function all in one piece." - Derbyshire
REFERENCES
John Derbyshire, Prime Obsession, Bernhard Riemann And The Greatest Unsolved Primblem In Mathematics, Joseph Henry Press, Washington, D.C., 2003, page 143.
EXAMPLE
a(9) = 34 because between -19 and -21, (at -19.403133257176569932332310530627...), =~ -33.80830359565166465388882152774755514487136542215568...),
MATHEMATICA
Table[ Round[ 1/FindMinimum[ 1/Abs[ Zeta[s]], {s, -2t - 1 + {-0.9, +0.9}}, AccuracyGoal -> 50, WorkingPrecision -> 60] [[1]]], {t, 1, 30}]
CROSSREFS
KEYWORD
sign
AUTHOR
Robert G. Wilson v, May 23 2003
STATUS
approved