File:GramPointsSinThetaZ 0 50.png
GramPointsSinThetaZ_0_50.png (360 × 221 pixels, file size: 14 KB, MIME type: image/png)
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editDescriptionGramPointsSinThetaZ 0 50.png |
Deutsch: Die Funktionen Sin(Theta(t)), blau, und Z(t), fliederfarben, für 0<t<50. Dabei ist Theta die Riemann-Siegelsche Theta-Funktion, Sin die Sinusfunktion und Z ist Hardys Z-Funktion. Die Nullstellen der blauen Kurven sind Gram-Punkte. Die Nullstellen der fliederfarbenen Kurve sind identisch mit den Imaginärteilen der Nullstellen der Riemannschen Zeta-Funktion auf der kritischen Geraden. Dieses Bild zeigt, dass sich im Bereich 5<t<50 die Nullstellen dieser beiden Kurven abwechseln. English: The functions Sin(Theta(t)), blue, and Z(t), lilac, for 0<t<50. Theta is the Riemann-Siegel theta function, Sin the sine function and Z is the Hardy Z-function (a.k.a. Riemann-Siegel Z-function). The zeros of the blue curve are Gram points. The zeros of the lilac curve coincide with the imaginary parts of zeros of the Riemann zeta function on the critical line. This picture is to show that, for 5<t<50, the zeros of these two curves separate each other. |
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Source | Own work |
Author | Chrgue |
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current | 23:01, 23 November 2013 | 360 × 221 (14 KB) | Chrgue (talk | contribs) | User created page with UploadWizard |
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