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The theory of elliptic curves is distinguished by its long history and by the diversity of the
methods that have been used in its study. This book treats the arithmetic theory of elliptic …

The purpose of this book is to develop the foundations of potential theory and rational
dynamics on the Berkovich projective line over an arbitrary complete, algebraically closed …

The 3x + 1 Problem: An Overview Page 1 The 3x + 1 Problem: An Overview Jeffrey C.
Lagarias 1. Introduction The 3x + 1 problem concerns the following innocent seeming …

Diophantine number theory is an active area that has seen tremendous growth over the past
century, and in this theory unit equations play a central role. This comprehensive treatment …

Starting from physical motivations and leading to practical applications, this book provides
an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential …

Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic
exposition of the theory of local iterated function systems, local fractal functions and fractal …

In this paper, we establish a theory of adelic line bundles over quasi-projective varieties over
finitely generated fields. Besides definitions of adelic line bundles, we consider their …

We study algebraic dynamical systems (and, more generally, σ-varieties) Φ:A^n_C→A^n_C
given by coordinatewise univariate polynomials by refining an old theorem of Ritt on …

Galois representations from pre-image trees: an arboreal survey Page 1 GALOIS
REPRESENTATIONS FROM PRE-IMAGE TREES: AN ARBOREAL SURVEY by Rafe Jones …