scholarly journals Integral points on the complement of the branch locus of projections from hypersurfaces

2017 ◽  
Vol 28 (2) ◽  
pp. 277-291
Author(s):  
Andrea Ciappi
Keyword(s):  
Branch Locus ◽  
Integral Points

Double cover K3 surfaces of Hirzebruch surfaces

2021 ◽  
Vol 21 (2) ◽  
pp. 221-225
Author(s):  
Taro Hayashi
Keyword(s):  
Rational Surface ◽  
K3 Surfaces ◽  
Double Cover ◽  
Double Covering ◽  
Smooth Surfaces ◽  
Branch Locus ◽  
Hirzebruch Surfaces ◽  
Double Covers

Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

scholarly journals On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
WonTae Hwang ◽  
Kyunghwan Song
Keyword(s):  
Zeta Function ◽  
Rational Number ◽  
Riemann Zeta Function ◽  
Rational Numbers ◽  
Critical Strip ◽  
Integer Part ◽  
Integral Points ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Abstract We prove that the integer part of the reciprocal of the tail of $\zeta (s)$ ζ ( s ) at a rational number $s=\frac{1}{p}$ s = 1 p for any integer with $p \geq 5$ p ≥ 5 or $s=\frac{2}{p}$ s = 2 p for any odd integer with $p \geq 5$ p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\frac{2}{p}$ s = 2 p , we use a result on the finiteness of integral points of certain curves over $\mathbb{Q}$ Q .

scholarly journals Integral points on hyperelliptic curves

2008 ◽  
Vol 2 (8) ◽  
pp. 859-885 ◽  
Author(s):  
Yann Bugeaud ◽  
Maurice Mignotte ◽  
Samir Siksek ◽  
Michael Stoll ◽  
Szabolcs Tengely
Keyword(s):  
Hyperelliptic Curves ◽  
Integral Points

scholarly journals F -structures and integral points on semiabelian varieties over finite fields

2004 ◽  
Vol 126 (3) ◽  
pp. 473-522 ◽  
Author(s):  
Rahim Moosa ◽  
Thomas Scanlon
Keyword(s):  
Finite Fields ◽  
Integral Points

scholarly journals On the Zariski-density of integral points on a complement of hyperplanes in Pn

2008 ◽  
Vol 128 (1) ◽  
pp. 96-104 ◽  
Author(s):  
Aaron Levin
Keyword(s):  
Integral Points

scholarly journals Integral Points on Subvarieties of Semiabelian Varieties, II

1999 ◽  
Vol 121 (2) ◽  
pp. 283-313 ◽  
Author(s):  
Paul Vojta
Keyword(s):  
Integral Points

scholarly journals Computing integral points on hyperelliptic curves using quadratic Chabauty

2016 ◽  
Vol 86 (305) ◽  
pp. 1403-1434 ◽  
Author(s):  
Jennifer S. Balakrishnan ◽  
Amnon Besser ◽  
J. Steffen Müller
Keyword(s):  
Hyperelliptic Curves ◽  
Integral Points

scholarly journals Generators and integral points on certain quartic curves

2019 ◽  
Vol 54 (2) ◽  
pp. 321-343
Author(s):  
Yasutsugu Fujita ◽  
◽  
Tadahisa Nara ◽  
Keyword(s):  
Integral Points ◽  
Quartic Curves

scholarly journals INTEGRAL POINTS ON THE CHEBYSHEV DYNAMICAL SYSTEMS

2015 ◽  
Vol 52 (5) ◽  
pp. 955-964
Author(s):  
SU-ION IH
Keyword(s):  
Dynamical Systems ◽  
Integral Points

scholarly journals Arithmetic purity of strong approximation for semi-simple simply connected groups

2020 ◽  
Vol 156 (12) ◽  
pp. 2628-2649
Author(s):  
Yang Cao ◽  
Zhizhong Huang
Keyword(s):  
Quadratic Form ◽  
Strong Approximation ◽  
Homogeneous Spaces ◽  
Algebraic Groups ◽  
Integral Points ◽  
Spin Group ◽  
Linear Algebraic Groups ◽  
Simply Connected ◽  
Quadratic Hypersurfaces ◽  
Almost Prime

In this article we establish the arithmetic purity of strong approximation for certain semisimple simply connected linear algebraic groups and their homogeneous spaces over a number field $k$. For instance, for any such group $G$ and for any open subset $U$ of $G$ with ${\mathrm {codim}}(G\setminus U, G)\geqslant 2$, we prove that (i) if $G$ is $k$-simple and $k$-isotropic, then $U$ satisfies strong approximation off any finite number of places; and (ii) if $G$ is the spin group of a non-degenerate quadratic form which is not compact over archimedean places, then $U$ satisfies strong approximation off all archimedean places. As a consequence, we prove that the same property holds for affine quadratic hypersurfaces. Our approach combines a fibration method with subgroup actions developed for induction on the codimension of $G\setminus U$, and an affine linear sieve which allows us to produce integral points with almost-prime polynomial values.

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