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In 2018, with Brad Rodgers, Tao showed that the de Bruijn–Newman constant, the nonpositivity of which is equivalent to the Riemann hypothesis, is nonnegative. [32] In 2020, Tao proved Sendov's conjecture , concerning the locations of the roots and critical points of a complex polynomial, in the special case of polynomials with sufficiently ...
Since the Riemann hypothesis is equivalent to the claim that all the zeroes of H(0, z) are real, the Riemann hypothesis is equivalent to the conjecture that Λ ≤ 0. Brad Rodgers and Terence Tao discovered the equivalence is actually Λ = 0 by proving zero to be the lower bound of the constant. [16]
The constant is closely connected with Riemann hypothesis. Indeed, the Riemann hypothesis is equivalent to the conjecture that . [1] Brad Rodgers and Terence Tao proved that , so the Riemann hypothesis is equivalent to =. [2] A simplified proof of the Rodgers–Tao result was later given by Alexander Dobner. [3]
In September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. ... If the Riemann Hypothesis were solved tomorrow, it would unlock an ...
Here is a sketch of the proof referred to in one of Terence Tao's lectures. [15] ... One can even prove an analogue of the Riemann hypothesis, namely that
In 2016, Terence Tao published a paper titled "Finite time blowup for an averaged three-dimensional Navier–Stokes equation", in which he formalizes the idea of a "supercriticality barrier" for the global regularity problem for the true Navier–Stokes equations, and claims that his method of proof hints at a possible route to establishing ...
One of his notable achievements is proving that the Riemann hypothesis is true up to 3 × 10 12. [3] In 2024, together with Terence Tao and Andrew Yang, Trudgian published an on-going database of known theorems for various exponents appearing in analytic number theory, named Analytic Number Theory Exponent Database (ANTEDB) , which could be ...
Riemann hypothesis: number theory: ⇐Generalized Riemann hypothesis⇐Grand Riemann hypothesis ⇔De Bruijn–Newman constant=0 ⇒density hypothesis, Lindelöf hypothesis See Hilbert–Pólya conjecture. For other Riemann hypotheses, see the Weil conjectures (now theorems). Bernhard Riemann: 24900 Ringel–Kotzig conjecture: graph theory