Roth's theorem on arithmetic progressions is a result in additive combinatorics concerning the existence of arithmetic progressions in subsets of the...

In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured...

Roth's theorem on arithmetic progressions". arXiv:2007.03528 [math.NT]. Kelley, Zander; Meka, Raghu (2023-11-06). "Strong Bounds for 3-Progressions"...

Friedrich Roth FRS (29 October 1925 – 10 November 2015) was a German-born British mathematician who won the Fields Medal for proving Roth's theorem on the Diophantine...

theorem on the density of sets of integers that avoid longer arithmetic progressions. To distinguish Roth's bound on Salem–Spencer sets from Roth's theorem...

prime, Dirichlet's theorem on arithmetic progressions asserts that the progression contains infinitely many primes. The Green–Tao theorem shows that there...

Dirichlet's theorem on arithmetic progressions Hurwitz's theorem (number theory) Heilbronn set Kronecker's theorem (generalization of Dirichlet's theorem) Schmidt...

theorem follows from the multidimensional corners theorem by a simple projection argument. In particular, Roth's theorem on arithmetic progressions follows...

Olof (2021-09-01). "Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions". arXiv:2007.03528 [math.NT]. Spalding, Katie (11 March...

Szemerédi proved the lemma over bipartite graphs for his theorem on arithmetic progressions in 1975 and for general graphs in 1978. Variants of the lemma...

obtained in the mid-1960s, concerning the distribution of primes in arithmetic progressions, averaged over a range of moduli. The first result of this kind...

Roth's theorem on 3-term arithmetic progressions, and a generalization of it, the hypergraph removal lemma, can be used to prove Szemerédi's theorem....

arithmetic progressions (number theory) Dirichlet's unit theorem (algebraic number theory) Equidistribution theorem (ergodic theory) Erdős–Kac theorem (number...

the arithmetic progressions. Overbay, Shawn; Schorer, Jimmy; Conger, Heather. "Al-Khwarizmi". University of Kentucky. Archived from the original on June...

Dirichlet's theorem on arithmetic progressions Linnik's theorem Elliott–Halberstam conjecture Functional equation (L-function) Chebotarev's density theorem Local...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

Among other results, he has improved the theorem of Klaus Friedrich Roth on three-term arithmetic progressions, coming close to breaking the so-called...

discrepancy theory The theorem of van Aardenne-Ehrenfest Arithmetic progressions (Roth, Sarkozy, Beck, Matousek & Spencer) Beck–Fiala theorem Six Standard Deviations...

of Beck. Earlier results on this problem include the famous lower bound on the discrepancy of arithmetic progressions by Roth and upper bounds for this...

stochastic matrix. 1985: Jozsef Beck for tight bounds on the discrepancy of arithmetic progressions. H. W. Lenstra Jr. for using the geometry of numbers...

on hypergraphs and established an upper bound on the discrepancy of the family of arithmetic progressions contained in {1,2,...,n}, matching the classical...

first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem. Don Zagier referred to the plaque as a "quantized Fields Medal". Accounts...

school. At the same time, these progressions signal the end of tonality. The first extended composition consistently based on symmetrical pitch relations...

integers can be without containing a k-term arithmetic progression, with upper bounds on this size given by Roth ( k = 3 {\displaystyle k=3} ) and Szemerédi...

large Salem–Spencer sets, sets of integers with no three forming an arithmetic progression. However, it does not work well to use this same idea of choosing...

(PDF) from the original on 22 April 2024. Retrieved 2 July 2024. "Royal Society – Sylvester Medal". Archived from the original on 2014-10-19. Retrieved...

based on purely rational slopes that only approximate the golden ratio. The Egyptians of those times apparently did not know the Pythagorean theorem; the...