Number Theory – Diophantine Problems, Uniform Distribution and Applications

Festschrift in Honour of Robert F. Tichy’s 60th Birthday

Christian Elsholtz, Peter Grabner

• Publisher: Springer
• Year: 2017
• Print ISBN:
  9783319553566
• eBook ISBN:
  9783319553573
• Topic: Mathematics
• Subtopic: Number Theory
• Index: Mathematics

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.

Table of contents

• Preface
• Contents
• List of Contributors
• On Nearly Linear Recurrence Sequences
• Risk Theory with Affine Dividend Payment Strategies
• A Discrepancy Problem: Balancing Infinite Dimensional Vectors
• Squares with Three Nonzero Digits
• On the Density of Coprime Tuples of the Form (n,⌊ f1(n)⌋,…,⌊ fk(n)⌋), Where f1,…,fk Are Functions from a Hardy Field
• On the Uniform Theory of Lacunary Series
• Diversity in Parametric Families of Number Fields
• Local Oscillations in Moderately Dense Sequences of Primes
• Sums of the Digits in Bases 2 and 3
• On the Discrepancy of Halton–Kronecker Sequences
• More on Diophantine Sextuples
• Effective Results for Discriminant Equations over Finitely Generated Integral Domains
• Quasi-Equivalence of Heights and Runge's Theorem
• On the Monoid Generated by a Lucas Sequence
• Measures of Pseudorandomness: Arithmetic Autocorrelation and Correlation Measure
• On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields
• Refined Estimates for Exponential Sums and a Problem Concerning the Product of Three L-Series
• Orbits of Algebraic Dynamical Systems in Subgroups and Subfields
• Patterns of Primes in Arithmetic Progressions
• On Simple Linear Recurrences
• Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures
• Discrepancy Bounds for β-adic Halton Sequences