Concept

Glossary of arithmetic and diophantine geometry

Publications associées (9)

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Unlikely intersections on the p-adic formal ball

Vlad Serban

We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...

SPRINGER INT PUBL AG2023

A Local Law for Singular Values from Diophantine Equations

Marius Christopher Lemm

We introduce the

N\times N

random matrices

X_{j,k}=\exp\left(2\pi i \sum_{q=1}^d\ \omega_{j,q} k^q\right) \quad \text{with } \{\omega_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \text{ i.i.d. random variables},

and

d

a fixed integer. We pr ...

2020

Height of rational points on quadratic twists of a given elliptic curve

Pierre Francis André Le Boudec

We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can prove only partial resul ...

Oxford Univ Press2016

Diophantine properties of nilpotent Lie groups

A finitely generated subgroup F of a real Lie group G is said to be Diophantine if there is beta > 0 such that non-trivial elements in the word ball B-Gamma(n) centered at 1 is an element of F never approach the identity of G closer than broken vertical ba ...

London Mathematical Society, Cambridge2015

Irregular primes and Cyclotomic Invariants to Twelve Million

Mohammad Amin Shokrollahi

Computations of irregular primes and associated cyclotomic invariants were extended to all primes up to twelve million using multisectioning/convolution methods and a novel approach which originated in the study of Stickelberger codes (Shokrollahi (1996)). ...

2001

Solving a system of linear diophantine equations with lower and upper bounds on the variables

Arjen Lenstra

We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It first finds a short vector satisfying the system of diophantine equations, and a set o ...

INFORMS2000

Market split and basis reduction: towards a solution of the Cornuejols-Dawande instances

Arjen Lenstra

Previously, G. Cornuejols and M. Dawande (1998) proposed a set of 0-1 linear programming instances that proved to be very hard to solve by traditional methods, and in particular by linear programming based branch-and-bound. They offered these market split ...

2000

Stickelberger Codes

Mohammad Amin Shokrollahi

Let

p

be an odd prime and

zeta_p

be a primitive pth root of unity over

smallBbbQ

. The Galois group

G

K:=smallBbbQ(zeta_p)

over

smallBbbQ

is a cyclic group of order

p-1

. The integral group ring

smallBbbZ[G]

contains the Stickelberger idea ...

1996

Wavelets and Filter Banks: Theory and Design

Martin Vetterli

The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, filter banks, and multiresolution signal processing are explored. A brief review is given of perfect re ...

1992

Stickelberger Codes

Mohammad Amin Shokrollahi

Let

p

be an odd prime and

zeta_p

be a primitive pth root of unity over

smallBbbQ

. The Galois group

G

K:=smallBbbQ(zeta_p)

over

smallBbbQ

is a cyclic group of order

p-1

. The integral group ring

smallBbbZ[G]

contains the Stickelberger idea ...

1996

A Local Law for Singular Values from Diophantine Equations

Marius Christopher Lemm

We introduce the

N\times N

random matrices

X_{j,k}=\exp\left(2\pi i \sum_{q=1}^d\ \omega_{j,q} k^q\right) \quad \text{with } \{\omega_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \text{ i.i.d. random variables},

and

d

a fixed integer. We pr ...

2020