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Publications associées (37)
A decomposition of multicorrelation sequences for commuting transformations along primes
A decomposition of multicorrelation sequences for commuting transformations along primes, Discrete Analysis 2021:4, 27 pp. Szemerédi's theorem asserts that for every positive integer and every there exists such that every subset of ${1, ...
2021Single and multiple recurrence along non-polynomial sequences
We establish new recurrence and multiple recurrence results for a rather large family of non-polynomial functions which contains tempered functions and (non-polynomial) functions from a Hardy field with polynomial growth. In particular, we show that, somew ...
2020Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications
We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...
2020Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited
Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...
Duke Univ Press2016Considerations for Rank-based Cryptosystems
Anna-Lena Horlemann, Joachim Rosenthal
Cryptosystems based on rank metric codes have been considered as an alternative to McEliece cryptosystems due to the relative difficulty of solving the rank syndrome decoding problem. Generic attacks have recently seen several improvements, notably in the ...
Ieee2016Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets
We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is ...
Elsevier2015