Riemann hypothesis for curves over finite fields

(For example, it was his letter that led Roosevelt to startthe Manhattan Project.)Among his many famous quotations is:"The search for truth is more precious than its possession."Einstein is most famous for his Special and General Theoriesof Relativity, but he should be considered the key pioneer ofQuantum Theory as well, drawing inferences from Planck's work thatno one else dared to draw.

The Riemann zeta function can be factored over its nontrivial zeros  as the

Turing also worked in group theory, numerical analysis,and complex analysis; he developed animportant theorem about Riemann's zeta function;he had novel insights in quantum physics.


Weil's work on the Riemann hypothesis for curves over ..

Farmer, D. W. "Counting Distinct Zeros of the Riemann Zeta-Function." 2, No. 1, R1, 1-5, 1995. .

He also proved that the Axioms of Choice (AC) and the Generalized ContinuumHypothesis (GCH) were with set theory, but that settheory's own consistency could not be proven.


Applications of Riemann and Extended Riemann Hypothesis

He also did seminal work with Riemann's zeta function,Dedekind's zeta functions,transcendental number theory, discontinuous groups,the 3-body problem in celestial mechanics,and symplectic geometry.

Riemann Zeta Function Zeros -- from Wolfram …

He introduced the Hilbert-Pólya Conjecture that theRiemann Hypothesis might be a consequence of spectral theory(in 2017 this Conjecture was partially proved by a team ofphysicists, and the Riemann Hypothesis be closeto solution!).

Zeros of the Riemann zeta function zeta(s) ..

Later it was noticed that this claim translates to a true statementabout the Riemann zeta function, with which Ramanujan was unfamiliar.)Ramanujan's innate ability for algebraic manipulations equaled or surpassedthat of Euler and Jacobi.

Riemann_hypothesis : definition of Riemann_hypothesis …

Much of his best work was done in collaboration with Hardy, for examplea proof that almost all numbers have about prime factors (a result which developed into probabilistic number theory).

The Dynamical Basis of the Riemann Hypothesis - …

He worked with the Prime Number Theorem and Riemann's Hypothesis;and proved the unexpected fact that Chebyshev's bias, and, while true for most, and all butvery large, numbers, are violated infinitely often.

Will Big Data solve the Riemann Hypothesis? - Data …

In addition to simpler proofs of existing theorems, new theorems by Landauinclude important facts about Riemann's Hypothesis;facts about Dirichlet series;key lemmas of analysis;a result in Waring's Problem;a generalization of the Little Picard Theorem;a partial proof of Gauss' conjecture about the density of classesof composite numbers;and key results in the theory of pecking orders, e.g.