Multiplicatively large sets and ergodic Ramsey theory
By utilizing various ergodic multiple recurrence theorems (e.g., of \textit{H. Furstenberg} and \textit{Y. Katznelson} [``An ergodic Szemerédi theorem for IP-systems and combinatorial theory'', J. Anal. Math. 45, 117--168 (1985; Zbl 0605.28012)] and \textit{V. Bergelson} and \textit{R. McCutcheon} [``An ergodic IP polynomial Szemerédi theorem'', Mem. Am. Math. Soc. 695, 106 (2000; Zbl 0948.28010)] various reswulte on multiplicatively large sets are proven, demonstrating their rich combinatorical structure. Such sets also contain various configurations which one expects to find in additively large sets, in particuliar arbitrary long arithmetic progressions. The author very well achieved a high level of readability making this paper, dedicated to Furstenberg on the occasion of his retirement, accesible to as wide an audience as possible.
scientific article; zbMATH DE number 5003404