Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, November 24, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Christian Elsholtz (TU Graz)

Hilbert cubes in arithmetic sets - or the complexity of squares

A Hilbert cube of dimension d is an iterated sumset H=a_0+{0,a_1}+ ... + {0, a_d}. Using such a cube one could store up to 2^d elements of the cube just by storing the d+1 base elements.

In this talk we prove an upper bound of d=O(log log N) on the maximal dimension d of the set of integer squares less than N. (Related results are possible, e.g. for k-th powers, pure powers, powerful numbers).

The proof combines methods from number theory and combinatorics.

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