1,1

"All these zeros of the form s + it have real part s = 1/2 and are simple. Thus the Riemann hypothesis is true at least for t < 3330657430697" - Wedeniwski

Contribution from Daniel Forgues (squid(AT)zensearch.com), Jul 24 2009: (Start)

All nontrivial zeros on the critical line, of the form 1/2 + i*t, have an associated conjugate nontrivial zero of the form 1/2 - i*t.

Any nontrivial zeros off the critical line, if ever found, would come in pairs (1/2 +/- delta) + i*t, 0 < delta < 1/2. Each of these pairs, again if ever found, would then have their associated conjugate pair (1/2 +/- delta) - i*t, 0 < delta < 1/2. (End)

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The imaginary parts of the first 4 zeros are 14.134725... (A058303), 21.0220396... (A065434), 25.01085758... (A065452), 30.424876... (A065453).

Cf. A013629, A058303, A057641, A057640, A058209, A058210, A120401, A122526.

Cf. A058303; A072080.

Cf. A124288 = "unstable" zeta zeros, A124289 = "unstable twins".

Sequence in context: A133185 A013629 A162780 this_sequence A108606 A129497 A093994

Adjacent sequences: A002407 A002408 A002409 this_sequence A002411 A002412 A002413

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004