arXiv subjects

John T. Griesmer

Publications and source records attributed to John T. Griesmer.

22 records · Page 2Linked to original sources

arXiv2010

Abundant configurations in sumsets with one dense summand

We analyze sumsets A+B = {a+b : a in A, b in B} where A,B are sets of integers, A is infinite, and B has positive upper Banach density. For each k, we show that A+B contains at least the expected density of k-term arithmetic progressions based on the density of B, in contrast with an example of Bergelson, Host, Kra, and Ruzsa. Furthermore, we show that A+B must contain finite configurations not necessarily found in arbitrary sets of positive density, in contrast with results of Frantzikinakis, Lesigne, and Wierdl on sets of k-recurrence.

math.DS↗

arXiv2010

Sumsets of dense sets and sparse sets

R. Jin showed that whenever A and B are sets of integers having positive upper Banach density, the sumset A+B is piecewise syndetic. This result was strengthened by Bergelson, Furstenberg, and Weiss to conclude that A+B must be piecewise Bohr. We generalize the latter result to cases where A has Banach density 0, giving a new proof of the previous results in the process.

math.DS↗

arXiv2008

Multiparameter ergodic averages for two commuting actions of an amenable group

We find limits of some multiple ergodic averages, generalizing a result of Bergelson to the setting of two commuting transformations and actions of amenable groups.

math.DS↗

arXiv2008

Cubic ergodic averages for actions of amenable groups

We unify and extend some previous results about cubic ergodic averages and sets of positive density in products of groups. This provides a joint generalization of earlier work of the author in the case of two commuting actions of an amenable group, and of Q. Chu's recent result on a a finite number of commuting transformations.

math.DS↗