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In mathematics, the Selberg conjecture, named after Atle Selberg, is a theorem about the density of zeros of the Riemann zeta function ζ(1/2 + it). It is known that the function has infinitely many zeroes on this line in the complex plane: the point at issue is how densely they are clustered. Results on this can be formulated in terms of N(T), the function counting zeroes on the line for which the value of t satisfies 0 ≤ t ≤ T.

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  • Conjecture de Selberg sur la fonction zêta (fr)
  • Selberg's zeta function conjecture (en)
  • Гипотеза Сельберга о дзета-функции (ru)
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  • In mathematics, the Selberg conjecture, named after Atle Selberg, is a theorem about the density of zeros of the Riemann zeta function ζ(1/2 + it). It is known that the function has infinitely many zeroes on this line in the complex plane: the point at issue is how densely they are clustered. Results on this can be formulated in terms of N(T), the function counting zeroes on the line for which the value of t satisfies 0 ≤ t ≤ T. (en)
  • En mathématiques, la conjecture de Selberg, du nom d'Atle Selberg, est un théorème sur la densité de zéros de la fonction zêta de Riemann ζ(1/2 + it). On sait que la fonction a une infinité de zéros sur cette ligne dans le plan complexe : le problème est de connaître leur répartition. Les résultats sur cela peuvent être formulés en fonction de N(T), la fonction de comptage des zéros sur la droite avec 0 ≤ t ≤ T. (fr)
  • Гипотеза Сельберга — математическая гипотеза о плотности нулей дзета-функции Римана ζ(1/2 + it), выдвинутая Атле Сельбергом. Гипотеза Сельберга является усилением второй гипотезы Харди—Литтлвуда.Сельберг выдвинул свою гипотезу, доказав гипотезу Харди—Литтлвуда. (ru)
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  • In mathematics, the Selberg conjecture, named after Atle Selberg, is a theorem about the density of zeros of the Riemann zeta function ζ(1/2 + it). It is known that the function has infinitely many zeroes on this line in the complex plane: the point at issue is how densely they are clustered. Results on this can be formulated in terms of N(T), the function counting zeroes on the line for which the value of t satisfies 0 ≤ t ≤ T. (en)
  • En mathématiques, la conjecture de Selberg, du nom d'Atle Selberg, est un théorème sur la densité de zéros de la fonction zêta de Riemann ζ(1/2 + it). On sait que la fonction a une infinité de zéros sur cette ligne dans le plan complexe : le problème est de connaître leur répartition. Les résultats sur cela peuvent être formulés en fonction de N(T), la fonction de comptage des zéros sur la droite avec 0 ≤ t ≤ T. (fr)
  • Гипотеза Сельберга — математическая гипотеза о плотности нулей дзета-функции Римана ζ(1/2 + it), выдвинутая Атле Сельбергом. Гипотеза Сельберга является усилением второй гипотезы Харди—Литтлвуда.Сельберг выдвинул свою гипотезу, доказав гипотезу Харди—Литтлвуда. (ru)
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