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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.…mehr
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.
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.
Inhaltsangabe
Preface.- Contents.- List of Contributors.- On Nearly Linear Recurrence Sequences, Shigeki Akiyama, Jan-Hendrik Evertse and Attila Pethö.- Risk Theory with Affine Dividend Payment Strategies, Hansjörg Albrecher and Arian Cani.- A Discrepancy Problem: Balancing Infinite Dimensional Vectors, József Beck.- Squares with Three Nonzero Digits, Michael A. Bennett and Adrian-Maria Scheerer.- On the density of coprime tuples of the form (n; bf1(n)c; : : : ; bfk(n)c), where f1; : : : ; fk are functions from a Hardy field, Vitaly Bergelson and Florian Karl Richter.- On the uniform theory of lacunary series, István Berkes.- Diversity in Parametric Families of Number Fields, Yuri Bilu and Florian Luca.- Local Oscillations in Moderately Dense Sequences of Primes, Jörg Brüdern and Christian Elsholtz.- Sums of the digits in bases 2 and 3, Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram and Bernard Landreau.- On the Discrepancy of Halton-Kronecker Sequences, Michael Drmota, Roswitha Hofer and Gerhard Larcher.- More on Diophantine Sextuples, Andrej Dujella and Matija Kazalicki.- Effective Results for Discrimant Equations Over Finitely Generated Integral Domains, Jan-Hendrik Evertse and Kálmán Györy.- Quasi-equivalence of Heights and Runge's Theorem, Philipp Habegger.- On the Monoid Generated by a Lucas Sequence, Clemens Heuberger and Stephan Wagner.- Measures of pseudorandomness: Arithmetic Autocorrelation and correlation Measure, Richard Hofer, László Mérai and Arne Winterhof.- On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields, Manfred G. Madritsch, Paul Surer and Volker Ziegler.- Refined Estimates for Exponential Sums and a Problem Concerning the Product of Three L-Series, Werner Georg Nowak.- Orbits of Algebraic Dynamical Systems in Subgroups and Subfields, Alina Ostafe and Igor E. Shparlinski.- Patterns of Primes in Arithmetic Progressions, János Pintz.- On Simple Linear Recurrences, Andrzej Schinzel.- Equivalence of theLogarithmically Averaged Chowla and Sarnak Conjectures, Terence Tao.- Discrepancy Bounds for -Adic Halton Sequences, Jörg M. Thuswaldner.
Preface.- Contents.- List of Contributors.- On Nearly Linear Recurrence Sequences, Shigeki Akiyama, Jan-Hendrik Evertse and Attila Pethö.- Risk Theory with Affine Dividend Payment Strategies, Hansjörg Albrecher and Arian Cani.- A Discrepancy Problem: Balancing Infinite Dimensional Vectors, József Beck.- Squares with Three Nonzero Digits, Michael A. Bennett and Adrian-Maria Scheerer.- On the density of coprime tuples of the form (n; bf1(n)c; : : : ; bfk(n)c), where f1; : : : ; fk are functions from a Hardy field, Vitaly Bergelson and Florian Karl Richter.- On the uniform theory of lacunary series, István Berkes.- Diversity in Parametric Families of Number Fields, Yuri Bilu and Florian Luca.- Local Oscillations in Moderately Dense Sequences of Primes, Jörg Brüdern and Christian Elsholtz.- Sums of the digits in bases 2 and 3, Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram and Bernard Landreau.- On the Discrepancy of Halton-Kronecker Sequences, Michael Drmota, Roswitha Hofer and Gerhard Larcher.- More on Diophantine Sextuples, Andrej Dujella and Matija Kazalicki.- Effective Results for Discrimant Equations Over Finitely Generated Integral Domains, Jan-Hendrik Evertse and Kálmán Györy.- Quasi-equivalence of Heights and Runge's Theorem, Philipp Habegger.- On the Monoid Generated by a Lucas Sequence, Clemens Heuberger and Stephan Wagner.- Measures of pseudorandomness: Arithmetic Autocorrelation and correlation Measure, Richard Hofer, László Mérai and Arne Winterhof.- On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields, Manfred G. Madritsch, Paul Surer and Volker Ziegler.- Refined Estimates for Exponential Sums and a Problem Concerning the Product of Three L-Series, Werner Georg Nowak.- Orbits of Algebraic Dynamical Systems in Subgroups and Subfields, Alina Ostafe and Igor E. Shparlinski.- Patterns of Primes in Arithmetic Progressions, János Pintz.- On Simple Linear Recurrences, Andrzej Schinzel.- Equivalence of theLogarithmically Averaged Chowla and Sarnak Conjectures, Terence Tao.- Discrepancy Bounds for -Adic Halton Sequences, Jörg M. Thuswaldner.
Preface.- Contents.- List of Contributors.- On Nearly Linear Recurrence Sequences, Shigeki Akiyama, Jan-Hendrik Evertse and Attila Pethö.- Risk Theory with Affine Dividend Payment Strategies, Hansjörg Albrecher and Arian Cani.- A Discrepancy Problem: Balancing Infinite Dimensional Vectors, József Beck.- Squares with Three Nonzero Digits, Michael A. Bennett and Adrian-Maria Scheerer.- On the density of coprime tuples of the form (n; bf1(n)c; : : : ; bfk(n)c), where f1; : : : ; fk are functions from a Hardy field, Vitaly Bergelson and Florian Karl Richter.- On the uniform theory of lacunary series, István Berkes.- Diversity in Parametric Families of Number Fields, Yuri Bilu and Florian Luca.- Local Oscillations in Moderately Dense Sequences of Primes, Jörg Brüdern and Christian Elsholtz.- Sums of the digits in bases 2 and 3, Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram and Bernard Landreau.- On the Discrepancy of Halton-Kronecker Sequences, Michael Drmota, Roswitha Hofer and Gerhard Larcher.- More on Diophantine Sextuples, Andrej Dujella and Matija Kazalicki.- Effective Results for Discrimant Equations Over Finitely Generated Integral Domains, Jan-Hendrik Evertse and Kálmán Györy.- Quasi-equivalence of Heights and Runge's Theorem, Philipp Habegger.- On the Monoid Generated by a Lucas Sequence, Clemens Heuberger and Stephan Wagner.- Measures of pseudorandomness: Arithmetic Autocorrelation and correlation Measure, Richard Hofer, László Mérai and Arne Winterhof.- On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields, Manfred G. Madritsch, Paul Surer and Volker Ziegler.- Refined Estimates for Exponential Sums and a Problem Concerning the Product of Three L-Series, Werner Georg Nowak.- Orbits of Algebraic Dynamical Systems in Subgroups and Subfields, Alina Ostafe and Igor E. Shparlinski.- Patterns of Primes in Arithmetic Progressions, János Pintz.- On Simple Linear Recurrences, Andrzej Schinzel.- Equivalence of theLogarithmically Averaged Chowla and Sarnak Conjectures, Terence Tao.- Discrepancy Bounds for -Adic Halton Sequences, Jörg M. Thuswaldner.
Preface.- Contents.- List of Contributors.- On Nearly Linear Recurrence Sequences, Shigeki Akiyama, Jan-Hendrik Evertse and Attila Pethö.- Risk Theory with Affine Dividend Payment Strategies, Hansjörg Albrecher and Arian Cani.- A Discrepancy Problem: Balancing Infinite Dimensional Vectors, József Beck.- Squares with Three Nonzero Digits, Michael A. Bennett and Adrian-Maria Scheerer.- On the density of coprime tuples of the form (n; bf1(n)c; : : : ; bfk(n)c), where f1; : : : ; fk are functions from a Hardy field, Vitaly Bergelson and Florian Karl Richter.- On the uniform theory of lacunary series, István Berkes.- Diversity in Parametric Families of Number Fields, Yuri Bilu and Florian Luca.- Local Oscillations in Moderately Dense Sequences of Primes, Jörg Brüdern and Christian Elsholtz.- Sums of the digits in bases 2 and 3, Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram and Bernard Landreau.- On the Discrepancy of Halton-Kronecker Sequences, Michael Drmota, Roswitha Hofer and Gerhard Larcher.- More on Diophantine Sextuples, Andrej Dujella and Matija Kazalicki.- Effective Results for Discrimant Equations Over Finitely Generated Integral Domains, Jan-Hendrik Evertse and Kálmán Györy.- Quasi-equivalence of Heights and Runge's Theorem, Philipp Habegger.- On the Monoid Generated by a Lucas Sequence, Clemens Heuberger and Stephan Wagner.- Measures of pseudorandomness: Arithmetic Autocorrelation and correlation Measure, Richard Hofer, László Mérai and Arne Winterhof.- On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields, Manfred G. Madritsch, Paul Surer and Volker Ziegler.- Refined Estimates for Exponential Sums and a Problem Concerning the Product of Three L-Series, Werner Georg Nowak.- Orbits of Algebraic Dynamical Systems in Subgroups and Subfields, Alina Ostafe and Igor E. Shparlinski.- Patterns of Primes in Arithmetic Progressions, János Pintz.- On Simple Linear Recurrences, Andrzej Schinzel.- Equivalence of theLogarithmically Averaged Chowla and Sarnak Conjectures, Terence Tao.- Discrepancy Bounds for -Adic Halton Sequences, Jörg M. Thuswaldner.
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