Polynomial mappings of groups
By Alexander Leibman. 2002
87 citations recorded by the source corpus.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ffc215c5a6ae7fefbdbb6dec5432c84c246fd7ab
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In Discrete Mathematics and Combinatorics
- Nikos Frantzikinakis
- B. Host
- M. N. Walsh
- Terence Tao
- Vitaly Bergelson
- Alexander Leibman
- Emmanuel Lesigne
- Q. Chu
In Geometry and Topology
- Nikos Frantzikinakis
- B. Host
- M. N. Walsh
- Vitaly Bergelson
- Alexander Leibman
- Terence Tao
- Emmanuel Lesigne
- T. Ziegler
In Mathematical Physics
- Nikos Frantzikinakis
- B. Host
- M. N. Walsh
- Terence Tao
- Vitaly Bergelson
- Alexander Leibman
- Emmanuel Lesigne
- Q. Chu
Citations in the corpus
- Multiple ergodic averages for three polynomials and applications (2006, unknown): “Given l 1 , . . . , l k ∈ N define the set It was shown in [22] that H is a closed sub-group of G k .”
- Distribution of values of bounded generalized polynomials (2007, background): “is piecewise polynomial if there is a partition B= L1 [...[Lr and polynomial mappings P1,...,Pr:R k !R l such that each Lj is defined by a system of polynomial inequalities and h|Lj =Pj, j=1,...,r.”
- Intersective polynomials and polynomial Szemeredi theorem (2007, background): “(n) ∈ H for all n ∈ Λ, then g is a P-polynomial sequence in H. Remark. Actually, the assertion of Proposition 4.1 holds for any (not necessarily topological) nilpotent group and any its subgroup (see [L1]). Proof. Replacing G by its universal cover we may assume that G is simply-connected. We then m”
- The Inverse Conjecture for the Gowers Norm over Finite Fields in Low Characteristic (2011, unknown): “A basic theorem of Lazard and Leibman [29], [30], [31] asserts that Poly(H → G) is a group; see e.”
- Norm convergence of nilpotent ergodic averages (2011, background): “We will make use of the following results of Leibman.”
- Higher order Fourier analysis of multiplicative functions and applications (2014, background): “The quantitative Leibman theorem.”
- Some open problems on multiple ergodic averages (2011, unknown): “ 67, 74, 78, 79, 91, 116, 120, 123, 132, 133, 138, 139, 146, 147, 149, 167, 168, 201, 213, 221, 222, 235, 250, 251, 255, 275, 284, 294, 296, 307]. Equidistribution on nilmanifolds and other nil-stuff: [17, 57, 88, 89, 90, 110, 109, 122, 131, 169, 170, 171, 175, 176, 177, 187, 188, 190, 192, 195, 196,”