Let G be a multiplicative subgroup of the prime field Fp of size |G| > p1−κ and r an arbitrarily fixed positive integer. Assuming κ = κ(r) > 0 and p large enough, it is shown that any proportional subset A ⊂ G contains non-trivial arithmetic progressions of length r. The main ingredient is the Szemerédi–Green–Tao theorem.
机构:
Inst Hautes Etud Sci, Le Bois Marie 35,Route Chartres, F-91440 Bures Sur Yvette, FranceInst Hautes Etud Sci, Le Bois Marie 35,Route Chartres, F-91440 Bures Sur Yvette, France
机构:
Middle East Tech Univ, Inst Appl Math, Ankara, TurkeyMiddle East Tech Univ, Inst Appl Math, Ankara, Turkey
Berktav, Kadri Ilker
Ozbudak, Ferruh
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机构:
Middle East Tech Univ, Inst Appl Math, Ankara, Turkey
Middle East Tech Univ, Dept Math, Ankara, TurkeyMiddle East Tech Univ, Inst Appl Math, Ankara, Turkey