Book contents
- Frontmatter
- Contents
- Preface
- 1 Some highlights of Harald Niederreiter's work
- 2 Partially bent functions and their properties
- 3 Applications of geometric discrepancy in numerical analysis and statistics
- 4 Discrepancy bounds for low-dimensional point sets
- 5 On the linear complexity and lattice test of nonlinear pseudorandom number generators
- 6 A heuristic formula estimating the keystream length for the general combination generator with respect to a correlation attack
- 7 Point sets of minimal energy
- 8 The cross-correlation measure for families of binary sequences
- 9 On an important family of inequalities of Niederreiter involving exponential sums
- 10 Controlling the shape of generating matrices in global function field constructions of digital sequences
- 11 Periodic structure of the exponential pseudorandom number generator
- 12 Construction of a rank-1 lattice sequence based on primitive polynomials
- 13 A quasi-Monte Carlo method for the coagulation equation
- 14 Asymptotic formulas for partitions with bounded multiplicity
- 15 A trigonometric approach for Chebyshev polynomials over finite fields
- 16 Index bounds for value sets of polynomials over finite fields
- 17 Rational points of the curve over
- 18 On the linear complexity of multisequences, bijections between ℤahlen and ℕumber tuples, and partitions
- Plate section
- References
1 - Some highlights of Harald Niederreiter's work
Published online by Cambridge University Press: 18 December 2014
Book contents
- Frontmatter
- Contents
- Preface
- 1 Some highlights of Harald Niederreiter's work
- 2 Partially bent functions and their properties
- 3 Applications of geometric discrepancy in numerical analysis and statistics
- 4 Discrepancy bounds for low-dimensional point sets
- 5 On the linear complexity and lattice test of nonlinear pseudorandom number generators
- 6 A heuristic formula estimating the keystream length for the general combination generator with respect to a correlation attack
- 7 Point sets of minimal energy
- 8 The cross-correlation measure for families of binary sequences
- 9 On an important family of inequalities of Niederreiter involving exponential sums
- 10 Controlling the shape of generating matrices in global function field constructions of digital sequences
- 11 Periodic structure of the exponential pseudorandom number generator
- 12 Construction of a rank-1 lattice sequence based on primitive polynomials
- 13 A quasi-Monte Carlo method for the coagulation equation
- 14 Asymptotic formulas for partitions with bounded multiplicity
- 15 A trigonometric approach for Chebyshev polynomials over finite fields
- 16 Index bounds for value sets of polynomials over finite fields
- 17 Rational points of the curve over
- 18 On the linear complexity of multisequences, bijections between ℤahlen and ℕumber tuples, and partitions
- Plate section
- References
Summary
Dedicated to our teacher, colleague and friend, Harald Niederreiter, on the occasion of his 70th birthday.
Abstract
In this paper we give a short biography of Harald Niederreiter and we spotlight some cornerstones from his wide-ranging work. We focus on his results on uniform distribution, algebraic curves, polynomials and quasi-Monte Carlo methods. In the flavor of Harald's work we also mention some applications including numerical integration, coding theory and cryptography.
A short biography
Harald Niederreiter was born in Vienna in 1944 on June 7 and spent his childhood in Salzburg. In 1963 he returned to Vienna to study at the Department of Mathematics of the University of Vienna, where he finished his PhD thesis entitled “Discrepancy in compact Abelian groups” sub auspiciis praesidentis rei publicae under the supervision of Edmund Hlawka in 1969. From 1969 to 1978 he worked as scientist and professor in the USA at four different institutes: Southern Illinois University, University of Illinois at Urbana-Champaign, Institute for Advanced Study, Princeton, and University of California at Los Angeles. From 1978 to 1981 he was Chair of Pure Mathematics at the University of the West Indies in Kingston (Jamaica). He returned to Austria and served as director of two institutes of the Austrian Academy of Sciences in Vienna, of the Institute for Information Processing until 1999 and then of the Institute of Discrete Mathematics. From 2001 to 2009 he was professor at the National University of Singapore. Since 2009 he has been located at the Johann Radon Institute for Computational and Applied Mathematics in Linz. From 2010 to 2011 he was professor at the King Fahd University of Petroleum and Minerals in Dhahran (Saudi Arabia).
Harald Niederreiter's research areas include numerical analysis, pseudorandom number generation, quasi-Monte Carlo methods, cryptology, finite fields, applied algebra, algorithms, number theory and coding theory. He has published more than 350 research papers and several books, including the following.
- Type
- Chapter
- Information
- Applied Algebra and Number Theory , pp. 1 - 21Publisher: Cambridge University PressPrint publication year: 2014
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