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30. Mai 2024 · In mathematics, the prime number theorem ( PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs.
1. Juni 2024 · As early as 1942, Atle Selberg proved using an ingenious method that a positive proportion of the nontrivial zeros are on the critical line. (“Positive proportion” means “more than 0%”.) To do this, Selberg developed a tool called the mollifier method.
Vor 6 Tagen · Atle Selberg investigated the problem of Hardy–Littlewood 2 and proved that for any ε > 0 there exists such = > and c = c(ε) > 0, such that for and = + the inequality (+) is true.
Vor 6 Tagen · He showed his formula to the mathematician Atle Selberg, who said that it looked like something in mathematical physics and that Montgomery should show it to Dyson, which he did.
24. Mai 2024 · points where S(t) changes sign. Similar results were obtained earlier for other conditions by Atle Selberg. Functional Equation. Riemann zeta function satisfies the following functional equation: ζ(s) = 2 s π s−1 sin(πs/2 ) Γ(1−s) ζ(1−s) where Γ(s) is Gamma Function
17. Mai 2024 · Some commentary on Atle Selberg's mathematics, Dennis Hejhal, Peter Sarnak Automorphic Forms and Applications, Ed. Peter Sarnak, Freydoon Shahidi, AS/Park City Mathematics Series, 12, AMS, 2007 Henryk Iwaniec, Peter Sarnak and Richard Taylor receive the 7th Ostrowski Prize; Problems of the Millennium: The Riemann Hypothesis, Peter Sarnak, 2004
11. Mai 2024 · Zhang Yitang replied, "I'm thinking about this now. Since Selberg (Norwegian mathematician Atle Selberg) defined a square method, I believe that many people have thought about it. Can I get rid of this square. On the Landau-Siegel zero problem, my key breakthrough is that I got rid of the square, and I can also prove that x(n) is not ...
