Sums with Kronecker sequence

Speaker: Nikolay Moshchevitin

1st August, 2pm, room 710.

Abstract:
I will tell you about old and recent results related to sums of the type ∑k=0Pt−1​f(αk+x) where f is a continuous function and α is an irrational number. Starting with an example by Poincaré (1888) we conclude with a recent paper of the speaker arXiv:2310.05003 and his student A. Chebotarenko arXiv:2502.19636. These results are related to phenomena which occur when f is/is not smooth (enough).
Also we deal with generalisations related to multidimensional Kronecker sequence.