Polynomial multiple recurrence over rings of integers

2014/09/26 by Bergelson, Vitaly, Robertson, Donald · 1 citation
#37A15 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.7569

Abstract

We generalize the polynomial Szemerédi theorem to intersective polynomials over the ring of integers of an algebraic number field, by which we mean polynomials having a common root modulo every ideal. This leads to the existence of new polynomial configurations in positive-density subsets of ℤ^m and strengthens and extends recent results of Bergelson, Leibman and Lesigne on polynomials over the integers.

Cited by

• Polynomial actions of rings of integers of global fields and quasirandomness of Paley-type graphs

Related

• Intersective polynomials and polynomial Szemeredi theorem
• Furstenberg--Sárközy theorem over number fields
• On the Polynomial Szemerédi Theorem in Finite Commutative Rings
• The polynomial analogue of a theorem of Renyi
• On polynomial progressions via transference