The Dynamical Mordell–Lang Conjecture

The Dynamical Mordell–Lang Conjecture
Author :
Publisher : American Mathematical Soc.
Total Pages : 297
Release :
ISBN-10 : 9781470424084
ISBN-13 : 1470424088
Rating : 4/5 (84 Downloads)

Synopsis The Dynamical Mordell–Lang Conjecture by : Jason P. Bell

The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point x under the action of an endomorphism f of a quasiprojective complex variety X. More precisely, it claims that for any point x in X and any subvariety V of X, the set of indices n such that the n-th iterate of x under f lies in V is a finite union of arithmetic progressions. In this book the authors present all known results about the Dynamical Mordell-Lang Conjecture, focusing mainly on a p-adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.

Nevanlinna Theory And Its Relation To Diophantine Approximation

Nevanlinna Theory And Its Relation To Diophantine Approximation
Author :
Publisher : World Scientific
Total Pages : 338
Release :
ISBN-10 : 9789814492485
ISBN-13 : 9814492485
Rating : 4/5 (85 Downloads)

Synopsis Nevanlinna Theory And Its Relation To Diophantine Approximation by : Min Ru

It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections. This book provides an introduction to both Nevanlinna theory and Diophantine approximation, with emphasis on the analogy between these two subjects.Each chapter is divided into part A and part B. Part A deals with Nevanlinna theory and part B covers Diophantine approximation. At the end of each chapter, a table is provided to indicate the correspondence of theorems.

The Dynamical Mordell-Lang Conjecture for Polynomial Endomorphisms of the Affine Plane

The Dynamical Mordell-Lang Conjecture for Polynomial Endomorphisms of the Affine Plane
Author :
Publisher :
Total Pages : 110
Release :
ISBN-10 : 2856298699
ISBN-13 : 9782856298695
Rating : 4/5 (99 Downloads)

Synopsis The Dynamical Mordell-Lang Conjecture for Polynomial Endomorphisms of the Affine Plane by : Junyi Xie

In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane over the algebraic numbers. More precisely, let f be an endomorphism of the affine plan over the algebraic numbers. Let x be a point in the affine plan and C be a curve. If the intersection of C and the orbits of x is infinite, then C is periodic.

Number Theory – Diophantine Problems, Uniform Distribution and Applications

Number Theory – Diophantine Problems, Uniform Distribution and Applications
Author :
Publisher : Springer
Total Pages : 447
Release :
ISBN-10 : 9783319553573
ISBN-13 : 3319553577
Rating : 4/5 (73 Downloads)

Synopsis Number Theory – Diophantine Problems, Uniform Distribution and Applications by : Christian Elsholtz

This volume is dedicated to Robert F. Tichy on the occasion of his 60th birthday. Presenting 22 research and survey papers written by leading experts in their respective fields, it focuses on areas that align with Tichy’s research interests and which he significantly shaped, including Diophantine problems, asymptotic counting, uniform distribution and discrepancy of sequences (in theory and application), dynamical systems, prime numbers, and actuarial mathematics. Offering valuable insights into recent developments in these areas, the book will be of interest to researchers and graduate students engaged in number theory and its applications.

Heights in Diophantine Geometry

Heights in Diophantine Geometry
Author :
Publisher : Cambridge University Press
Total Pages : 676
Release :
ISBN-10 : 0521712297
ISBN-13 : 9780521712293
Rating : 4/5 (97 Downloads)

Synopsis Heights in Diophantine Geometry by : Enrico Bombieri

This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.

Moduli Spaces and Arithmetic Dynamics

Moduli Spaces and Arithmetic Dynamics
Author :
Publisher : American Mathematical Soc.
Total Pages : 151
Release :
ISBN-10 : 9780821885031
ISBN-13 : 0821885030
Rating : 4/5 (31 Downloads)

Synopsis Moduli Spaces and Arithmetic Dynamics by : Joseph H. Silverman

The Mordell Conjecture

The Mordell Conjecture
Author :
Publisher : Cambridge University Press
Total Pages : 179
Release :
ISBN-10 : 9781108845953
ISBN-13 : 1108845959
Rating : 4/5 (53 Downloads)

Synopsis The Mordell Conjecture by : Hideaki Ikoma

This book provides a self-contained proof of the Mordell conjecture (Faltings's theorem) and a concise introduction to Diophantine geometry.

Diophantine Geometry

Diophantine Geometry
Author :
Publisher : Springer Science & Business Media
Total Pages : 574
Release :
ISBN-10 : 9781461212102
ISBN-13 : 1461212103
Rating : 4/5 (02 Downloads)

Synopsis Diophantine Geometry by : Marc Hindry

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Mathematical Logic in the 20th Century

Mathematical Logic in the 20th Century
Author :
Publisher : World Scientific
Total Pages : 712
Release :
ISBN-10 : 9812564896
ISBN-13 : 9789812564894
Rating : 4/5 (96 Downloads)

Synopsis Mathematical Logic in the 20th Century by : Gerald E. Sacks

This invaluable book is a collection of 31 important both inideas and results papers published by mathematical logicians inthe 20th Century. The papers have been selected by Professor Gerald ESacks. Some of the authors are Gdel, Kleene, Tarski, A Robinson, Kreisel, Cohen, Morley, Shelah, Hrushovski and Woodin.

Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties

Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties
Author :
Publisher : American Mathematical Soc.
Total Pages : 176
Release :
ISBN-10 : 9781470414580
ISBN-13 : 1470414589
Rating : 4/5 (80 Downloads)

Synopsis Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties by : Carlo Gasbarri

This volume contains papers from the Short Thematic Program on Rational Points, Rational Curves, and Entire Holomorphic Curves and Algebraic Varieties, held from June 3-28, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada. The program was dedicated to the study of subtle interconnections between geometric and arithmetic properties of higher-dimensional algebraic varieties. The main areas of the program were, among others, proving density of rational points in Zariski or analytic topology on special varieties, understanding global geometric properties of rationally connected varieties, as well as connections between geometry and algebraic dynamics exploring new geometric techniques in Diophantine approximation. This book is co-published with the Centre de Recherches Mathématiques.