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- Hardy–Littlewood_zeta-function_conjectures abstract "In mathematics, the Hardy–Littlewood zeta-function conjectures, named after Godfrey Harold Hardy and John Edensor Littlewood, are two conjectures concerning the distances between zeros and the density of zeros of the Riemann zeta function.In 1914 Godfrey Harold Hardy proved that the Riemann zeta function has infinitely many real zeros.Let be the total number of real zeros, be the total number of zeros of odd order of the function , lying on the interval.Hardy and Littlewood claimed two conjectures. These conjectures – on the distance between real zeros of and on the density of zeros of on intervals for sufficiently great , and with as less as possible value of , where is an arbitrarily small number – open two new directions in the investigation of the Riemann zeta function.1. For any there exists such that for and the interval contains a zero of odd order of the function .2. For any there exist and , such that for and the inequality is true.In 1942 Atle Selberg studied the problem 2 and proved that for any there exists such and , such that for and the inequality is true.In his turn, Selberg claim his conjecture that it's possible to decrease the value of the exponent for which was proved forty-two years later by A.A. Karatsuba.".
- Hardy–Littlewood_zeta-function_conjectures wikiPageID "31314347".
- Hardy–Littlewood_zeta-function_conjectures wikiPageRevisionID "569390865".
- Hardy–Littlewood_zeta-function_conjectures subject Category:Conjectures.
- Hardy–Littlewood_zeta-function_conjectures subject Category:Zeta_and_L-functions.
- Hardy–Littlewood_zeta-function_conjectures comment "In mathematics, the Hardy–Littlewood zeta-function conjectures, named after Godfrey Harold Hardy and John Edensor Littlewood, are two conjectures concerning the distances between zeros and the density of zeros of the Riemann zeta function.In 1914 Godfrey Harold Hardy proved that the Riemann zeta function has infinitely many real zeros.Let be the total number of real zeros, be the total number of zeros of odd order of the function , lying on the interval.Hardy and Littlewood claimed two conjectures. ".
- Hardy–Littlewood_zeta-function_conjectures label "Hardy–Littlewood zeta-function conjectures".
- Hardy–Littlewood_zeta-function_conjectures sameAs Hardy%E2%80%93Littlewood_zeta-function_conjectures.
- Hardy–Littlewood_zeta-function_conjectures sameAs Q15643131.
- Hardy–Littlewood_zeta-function_conjectures sameAs Q15643131.
- Hardy–Littlewood_zeta-function_conjectures wasDerivedFrom Hardy–Littlewood_zeta-function_conjectures?oldid=569390865.