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Now showing items 1-9 of 9

#### Maximal differential uniformity polynomials

(2017)

We provide an explicit infinite family of integers m such
that all the polynomials of F2n [x] of degree m have maximal differential
uniformity for n large enough. We also prove a conjecture of the third
author in these cases.

#### Relative Brauer groups of torsors of period two

(2016)

We consider the problem of computing the relative Brauer group of a torsor of
period two under an elliptic curve. We show how this problem can be reduced to finding a
set of generators for the group of rational points ...

#### Degree and the Brauer-Manin obstruction

(2017)

Let X be a smooth variety over a number field k embedded as a degree d
subvariety of {P}^nk and suppose that X is a counterexample to the
Hasse principle explained by the Brauer-Manin obstruction. We consider the
question ...

#### Value sets of sparse polynomials

(2018)

We obtain a new lower bound on the size of value set V (ƒ) = ƒ(Fp) of a sparse
polynomial ƒ ϵ Fp[X] over a finite field of p elements when p is prime. This
bound is uniform with respect of the degree and depends on some ...

#### Improved rank bounds from 2-descent on hyperelliptic Jacobians

(2018)

© 2018 World Scientific Publishing Company. We describe a qualitative improvement to the algorithms for performing 2-descents to obtain information regarding the Mordell-Weil rank of a hyperelliptic Jacobian. The improvement ...

#### Zero-cycles of degree one on Skorobogatov's bielliptic surface

(2017)

© 2017 Elsevier Inc. Skorobogatov constructed a bielliptic surface which is a counterexample to the Hasse principle not explained by the Brauer–Manin obstruction. We show that this surface has a 0-cycle of degree 1, as ...

#### Thinplate splines on the sphere

(2018)

© 2018, Institute of Mathematics. All rights reserved. In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate ...

#### Binomial exponential sums

(2018)

We obtain new bounds of exponential sums modulo a prime p with binomials
axk + bxn. In particular, for k=1, we improve the bound of Karatsuba
(1967) from O(n1/4 p3/4) to O(p3/4 + n1/3 p2/3)
for any n, and then use it ...

#### Tate-Shafarevich groups of constant elliptic curves and isogeny volcanos

(2019)

We describe the structure of Tate-Shafarevich groups of a constant elliptic curves over function fields by exploiting the volcano structure of isogeny graphs of elliptic curves over finite fields.