The Green-Tao theorem: an exposition
نویسندگان
چکیده
منابع مشابه
The Green-tao Theorem: an Exposition
The celebrated Green-Tao theorem states that the prime numbers contain arbitrarily long arithmetic progressions. We give an exposition of the proof, incorporating several simplifications that have been discovered since the original paper.
متن کاملNew Proofs of the Green–Tao–Ziegler Dense Model Theorem: An Exposition
Green, Tao and Ziegler [GT, TZ] prove “Dense Model Theorems” of the following form: if R is a (possibly very sparse) pseudorandom subset of set X , and D is a dense subset of R, then D may be modeled by a set M whose density inside X is approximately the same as the density of D in R. More generally, they show that a function that is majorized by a pseudorandom measure can be written as a sum o...
متن کاملGreen-tao Theorem in Function Fields
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every k, the irreducible polynomials in Fq[t] contain configurations of the form {f + P g : deg(P) < k}, g = 0.
متن کاملGreen-tao Theorem in Function Fields
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite fields, to show that for every k, the irreducible polynomials in Fq[t] contains configurations of the form {f + P g : deg(P) < k}, g = 0.
متن کاملSGGS Theorem Proving: an Exposition
We present in expository style the main ideas in SGGS, which stands for Semantically-Guided GoalSensitive theorem proving. SGGS uses sequences of constrained clauses to represent models, instance generation to go from a candidate model to the next, and resolution as well as other inferences to repair the model. SGGS is refutationally complete for first-order logic, DPLL-style model based, seman...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: EMS Surveys in Mathematical Sciences
سال: 2014
ISSN: 2308-2151
DOI: 10.4171/emss/6