## Search

Now showing items 1-8 of 8

#### The circle space of a spherical circle plane

(BELGIAN MATHEMATICAL SOC TRIOMPHE, 2014)

We show that the circle space of a spherical circle plane is a punctured
projective 3-space. The main ingredient is a partial solution of the problem
of Apollonius on common touching circles.

#### Maps between curves and arithmetic obstructions

(2017)

Let X and Y be curves over a finite field. In this article we explore methods
to determine whether there is a rational map from Y to X by considering
L-functions of certain covers of X and Y and propose a specific family ...

#### On automorphism groups of toroidal circle planes

(2018)

© 2018, Springer International Publishing AG, part of Springer Nature. Schenkel proved that the automorphism group of a flat Minkowski plane is a Lie group of dimension at most 6 and described planes whose automorphism ...

#### 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 ...

#### 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 ...

#### Three-dimensional connected groups of automorphisms of toroidal circle planes

(2018)

We contribute to the classification of toroidal circle planes and flat
Minkowski planes possessing three-dimensional connected groups of
automorphisms. When such a group is an almost simple Lie group, we show that it
is ...

#### 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 ...