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A084973
The maximum departure from the x axis, rounded to the nearest integer, in each cycle of the zeta function for increasingly larger negative values.
0
0, 0, 0, 0, 0, 0, -1, 4, -34, 374, -4988, 78674, -1449689, 30854707, -751125115, 20736542367, -644361764772, 22387174696660, -864494448030320, 36906142650945649, -1733457688501062507, 89187472319797248472
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
Sequence in context: A199752 A264607 A307941 * A234313 A367869 A369191
KEYWORD
sign
AUTHOR
Robert G. Wilson v, May 23 2003
STATUS
approved