Applied Algebra and Number Theory

Harald Niederreiter's pioneering research in the field of applied algebra and number theory has led to important and substantial breakthroughs in many areas. This collection of survey articles has been authored by close colleagues and leading experts to mark the occasion of his 70th birthday. The book provides a modern overview of different research areas, covering uniform distribution and quasi-Monte Carlo methods as well as finite fields and their applications, in particular, cryptography and pseudorandom number generation. Many results are published here for the first time. The book serves as a useful starting point for graduate students new to these areas or as a refresher for researchers wanting to follow recent trends.

Preface Gerhard Larcher, Friedrich Pillichshammer, Arne Winterhof and Chaoping Xing; 1. Some highlights of Harald Niederreiter's work Gerhard Larcher, Friedrich Pillichshammer, Arne Winterhof and Chaoping Xing; 2. Partially bent functions and their properties Ayça Çeşmelioğlu, Wilfried Meidl and Alev Topuzoğlu; 3. Applications of geometric discrepancy in numerical analysis and statistics Josef Dick; 4. Discrepancy bounds for low-dimensional point sets Henri Faure and Peter Kritzer; 5. On the linear complexity and lattice test of nonlinear pseudorandom number generators Domingo Gómez-Pérez and Jaime Gutierrez; 6. A heuristic formula estimating the keystream length for the general combination generator with respect to a correlation attack Rainer Göttfert; 7. Point sets of minimal energy Peter J. Grabner; 8. The cross-correlation measure for families of binary sequences Katalin Gyarmati, Christian Mauduit and András Sárközy; 9. On an important family of inequalities of Niederreiter involving exponential sums Peter Hellekalek; 10. Controlling the shape of generating matrices in global function field constructions of digital sequences Roswitha Hofer and Isabel Pirsic; 11. Periodic structure of the exponential pseudorandom number generator Jonas Kaszián, Pieter Moree and Igor E. Shparlinski; 12. Construction of a rank-1 lattice sequence based on primitive polynomials Alexander Keller, Nikolaus Binder and Carsten Wächter; 13. A quasi-Monte Carlo method for the coagulation equation Christian Lécot and Ali Tarhini; 14. Asymptotic formulae for partitions with bounded multiplicity Pierre Liardet and Alain Thomas; 15. A trigonometric approach for Chebyshev polynomials over finite fields Juliano B. Lima, Daniel Panario and Ricardo M. Campello de Souza; 16. Index bounds for value sets of polynomials over finite fields Gary L. Mullen, Daqing Wan and Qiang Wang; 17. Rational points of the curve yqn − y = γxqh+1 − α over Fqm Ferruh Özbudak and Zülfükar Saygi; 18. On the linear complexity of multisequences, bijections between Zahlen and number tuples, and partitions Michael Vielhaber.

Gerhard Larcher is Full Professor for Financial Mathematics and Head of the Institute for Financial Mathematics at the Johannes Kepler University Linz.
Friedrich Pillichshammer is Associate Professor in the Institute for Financial Mathematics at the Johannes Kepler University Linz.
Arne Winterhof is Senior Fellow at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) at the Austrian Academy of Sciences, Linz.
Chaoping Xing is Full Professor in the Department of Physical and Mathematical Sciences at Nanyang Technological University, Singapore.