Number Theory – Diophantine Problems, Uniform Distribution and Applications

1. Front Matter

   Pages i-xv

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2. On Nearly Linear Recurrence Sequences

   • Shigeki Akiyama, Jan-Hendrik Evertse, Attila Pethő

   Pages 1-24

3. Risk Theory with Affine Dividend Payment Strategies

   • Hansjörg Albrecher, Arian Cani

   Pages 25-60

4. A Discrepancy Problem: Balancing Infinite Dimensional Vectors

   • József Beck

   Pages 61-82

5. Squares with Three Nonzero Digits

   • Michael A. Bennett, Adrian-Maria Scheerer

   Pages 83-108

6. On the Density of Coprime Tuples of the Form (n, ⌊ f ₁(n)⌋, …, ⌊ f _k (n)⌋), Where f ₁, …, f _k Are Functions from a Hardy Field

   • Vitaly Bergelson, Florian Karl Richter

   Pages 109-135

7. On the Uniform Theory of Lacunary Series

   • István Berkes

   Pages 137-167

8. Diversity in Parametric Families of Number Fields

   • Yuri Bilu, Florian Luca

   Pages 169-191

9. Local Oscillations in Moderately Dense Sequences of Primes

   • Jörg Brüdern, Christian Elsholtz

   Pages 193-210

10. Sums of the Digits in Bases 2 and 3

    • Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram, Bernard Landreau

    Pages 211-217

11. On the Discrepancy of Halton–Kronecker Sequences

    • Michael Drmota, Roswitha Hofer, Gerhard Larcher

    Pages 219-226

12. More on Diophantine Sextuples

    • Andrej Dujella, Matija Kazalicki

    Pages 227-235

13. Effective Results for Discriminant Equations over Finitely Generated Integral Domains

    • Jan-Hendrik Evertse, Kálmán Győry

    Pages 237-256

14. Quasi-Equivalence of Heights and Runge’s Theorem

    • Philipp Habegger

    Pages 257-280

15. On the Monoid Generated by a Lucas Sequence

    • Clemens Heuberger, Stephan Wagner

    Pages 281-301

16. Measures of Pseudorandomness: Arithmetic Autocorrelation and Correlation Measure

    • Richard Hofer, László Mérai, Arne Winterhof

    Pages 303-312

17. On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields

    • Manfred G. Madritsch, Paul Surer, Volker Ziegler

    Pages 313-332

18. Refined Estimates for Exponential Sums and a Problem Concerning the Product of Three L-Series

    • Werner Georg Nowak

    Pages 333-345

19. Orbits of Algebraic Dynamical Systems in Subgroups and Subfields

    • Alina Ostafe, Igor E. Shparlinski

    Pages 347-368

20. Patterns of Primes in Arithmetic Progressions

    • János Pintz

    Pages 369-379

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.

• diophantine equations
• uniform distribution of sequences and discrepancy
• digit representation of integer sequences
• primes
• actuarial mathematics
• number theory

• Institute of Analysis and Number Theory, Graz University of Technology, Graz, Austria

  Christian Elsholtz, Peter Grabner

Christian Elsholtz is Associate Professor at the Graz University of Technology, Institute of Analysis and Number Theory.

Peter Grabner is Professor at the Graz University of Technology, Institute of Analysis and Number Theory.

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