Maximal differential uniformity polynomials

Recurrence and Non-uniformity of Bracket Polynomials

In his celebrated proof of Szemerédi’s theorem that a set of integers of positive density contains arbitrarily long arithmetic progressions, W. T. Gowers introduced a certain sequence of norms ‖ · ‖U 2[N ] ≤ ‖ · ‖U 3[N ] ≤ . . . on the space of complex-valued functions on the set [N ]. An important question regarding these norms concerns for which functions they are ‘large’ in a certain sense. ...

Fractional differential equations with Legendre polynomials

Maximal and Linearly Inextensible Polynomials

Let S(n, 0) be the set of monic complex polynomials of degree n ≥ 2 having all their zeros in the closed unit disk and vanishing at 0. For p ∈ S(n, 0) denote by |p|0 the distance from the origin to the zero set of p. We determine all 0-maximal polynomials of degree n, that is, all polynomials p ∈ S(n, 0) such that |p|0 ≥ |q|0 for any q ∈ S(n, 0). Using a second order variational method we then ...

Uniformity of the Meager Ideal and Maximal Coonitary Groups

We prove that every maximal coonitary group has size at least the cardinality of the smallest non{meager set of reals. We also provide a consistency result saying that the spectrum of possible cardinalities of maximal coonitary groups may be quite arbitrary.

Differential Spectrum of Some Power Functions With Low Differential Uniformity

In this paper, for an odd prime p, the differential spectrum of the power function x pk+1 2 in Fpn is calculated. For an odd prime p such that p ≡ 3 mod 4 and odd n with k|n, the differential spectrum of the power function x pn+1 pk+1 + p n −1 2 in Fpn is also derived. From their differential spectrums, the differential uniformities of these two power functions are determined. We also find some...