Qurak

ZetaZero

Available

The k-th nontrivial zero of the Riemann zeta function on the critical line, counting upward from the real axis; the two-argument form starts the search above imaginary part t.

Returned symbolically. Wrap it in `N` for a numeric value.

ZetaZero[k]
ZetaZero[k, t]
Zeta[ZetaZero[10]] → 0Plot[Im[Zeta[1 / 2 + I z]], {z, 0, 32}, Epilog -> {PointSize[0.03], Red, Point[Table[{Im[ZetaZero[k]], 0}, {k, 4}]]}] → -Graphics-Plot[Im[Zeta[1 / 2 + I z]], {z, 0, 30}, Epilog -> {PointSize[0.03], Red, Point[{Im[ZetaZero[1, 15]], 0}]}] → -Graphics-

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