Applied Algebra and Number Theory

Gerhard Larcher, Friedrich Pillichshammer, Arne Winterhof, Chaoping Xing

• Publisher: Cambridge University Press
• Year: 2014
• Print ISBN: 9781107074002
• eBook ISBN: 9781316121641
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title page
• Frontispiece
• Title page
• Copyright page
• 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 y[sup(q)[sup(n)]]-y=x[sup(q)[sup(h)]][sup(+1)] -α over F[sub(q)sup(m)]
• 18 On the linear complexity of multisequences, bijections between Zahlen and Number tuples, and partitions