Applied Algebra and Number Theory

doi:10.1017/CBO9781139696456

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.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-x
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Preface
pp xi-xii
- By Arne Winterhof, Chaoping Xing, Nanyang Technological University, Singapore
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1 - Some highlights of Harald Niederreiter's work
pp 1-21
- By Gerhard Larcher, Johannes Kepler University Linz, Friedrich Pillichshammer, Johannes Kepler University Linz, Arne Winterhof, Austrian Acadamy of Sciences, Linz, Chaoping Xing, Nanyang Techological University, Singapore
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2 - Partially bent functions and their properties
pp 22-38
- By Ayça Çeşmelioğlu, Istanbul Kemerburgaz University, Istanbul, Wilfried Meidl, Sabanci University, Istanbul, Alev Topuzoğlu, Sabanci University, Istanbul
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3 - Applications of geometric discrepancy in numerical analysis and statistics
pp 39-57
- By Josef Dick, The University of New South Wales, Sydney
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4 - Discrepancy bounds for low-dimensional point sets
pp 58-90
- By Henri Faure, Aix Marseille University, Marseille, Peter Kritzer, Johannes Kepler University Linz
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5 - On the linear complexity and lattice test of nonlinear pseudorandom number generators
pp 91-101
- By Domingo Gómez-Pérez, University of Cantabria, Santander, Jaime Gutierrez, University of Cantabria, Santander
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6 - A heuristic formula estimating the keystream length for the general combination generator with respect to a correlation attack
pp 102-108
- By Rainer Göttfert, Infineon Technologies AG, Munich
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7 - Point sets of minimal energy
pp 109-125
- By Peter J. Grabner, Technische Universität, Graz
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8 - The cross-correlation measure for families of binary sequences
pp 126-143
- By Katalin Gyarmati, Eötvös Loránd University, Budapest, Christian Mauduit, Aix Marseille University, Marseille, András Sárközy, Eötvös Loránd University, Budapest
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9 - On an important family of inequalities of Niederreiter involving exponential sums
pp 144-163
- By Peter Hellekalek, Salzburg University, Salzburg
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10 - Controlling the shape of generating matrices in global function field constructions of digital sequences
pp 164-189
- By Roswitha Hofer, Johannes Kepler University Linz, Isabel Pirsic, Johannes Kepler University Linz
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11 - Periodic structure of the exponential pseudorandom number generator
pp 190-203
- By Jonas Kaszián, RWTH Aachen, Aachen, Pieter Moree, Max-Planck-Institut für Mathematik, Bonn, Igor E. Shparlinski, University of New South Wales, Sydney
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12 - Construction of a rank-1 lattice sequence based on primitive polynomials
pp 204-215
- By Alexander Keller, NVIDIA, Berlin, Nikolaus Binder, NVIDIA, Berlin, Carsten Wächter, NVIDIA, Berlin
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13 - A quasi-Monte Carlo method for the coagulation equation
pp 216-234
- By Christian Lécot, Université de Savoie, Le Bourget-du-Lac, Ali Tarhini, Université Libanaise, Nabatieh
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14 - Asymptotic formulas for partitions with bounded multiplicity
pp 235-254
- By Pierre Liardet, Aix Marseille University, Marseille, Alain Thomas, Aix Marseille University, Marseille
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15 - A trigonometric approach for Chebyshev polynomials over finite fields
pp 255-279
- By Juliano B. Lima, Federal University of Pernambuco, Recife, Daniel Panario, Carleton University, Ottawa, Ricardo M. Campello de Souza, Federal University of Pernambuco, Recife
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16 - Index bounds for value sets of polynomials over finite fields
pp 280-296
- By Gary L. Mullen, Pennsylvania State University, University Park, PA, Daqing Wan, University of California Irvine, CA, Qiang Wang, Carleton University, Ottawa
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17 - Rational points of the curve over
pp 297-306
- By Ferruh Özbudak, Middle East Technical University, Ankara, Zülfükar Saygı, TOBB, University of Economics and Technology, Ankara
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18 - On the linear complexity of multisequences, bijections between ℤahlen and ℕumber tuples, and partitions
pp 307-335
- By Michael Vielhaber, Hochschule Bremerhaven, Bremerhaven
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Plate section
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Applied Algebra and Number Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-x

Preface
pp xi-xii

1 - Some highlights of Harald Niederreiter's work
pp 1-21

2 - Partially bent functions and their properties
pp 22-38

3 - Applications of geometric discrepancy in numerical analysis and statistics
pp 39-57

4 - Discrepancy bounds for low-dimensional point sets
pp 58-90

5 - On the linear complexity and lattice test of nonlinear pseudorandom number generators
pp 91-101

6 - A heuristic formula estimating the keystream length for the general combination generator with respect to a correlation attack
pp 102-108

7 - Point sets of minimal energy
pp 109-125

8 - The cross-correlation measure for families of binary sequences
pp 126-143

9 - On an important family of inequalities of Niederreiter involving exponential sums
pp 144-163

10 - Controlling the shape of generating matrices in global function field constructions of digital sequences
pp 164-189

11 - Periodic structure of the exponential pseudorandom number generator
pp 190-203

12 - Construction of a rank-1 lattice sequence based on primitive polynomials
pp 204-215

13 - A quasi-Monte Carlo method for the coagulation equation
pp 216-234

14 - Asymptotic formulas for partitions with bounded multiplicity
pp 235-254

15 - A trigonometric approach for Chebyshev polynomials over finite fields
pp 255-279

16 - Index bounds for value sets of polynomials over finite fields
pp 280-296

17 - Rational points of the curve over
pp 297-306

18 - On the linear complexity of multisequences, bijections between ℤahlen and ℕumber tuples, and partitions
pp 307-335

Plate section

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Applied Algebra and Number Theory

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