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This volume is dedicated to Harvey Cohn, Distinguished Professor Emeritus of Mathematics at City College (CUNY). Harvey was one of the organizers of the New York Number Theory Seminar, and was deeply involved in all aspects of the Seminar from its first meeting in January, 1982, until his retirement in December, 1995. We wish him good health and continued hapiness and success in mathematics. The papers in this volume are revised and expanded versions of lectures delivered in the New York Number Theory Seminar. The Seminar meets weekly at the Graduate School and University Center of the City University of New York (CUNY). In addition, some of the papers in this book were presented at a conference on Combinatorial Number Theory that the New York Number Theory Seminar organized at Lehman College (CUNY). Here is a short description of the papers in this volume. The paper of R. T. Bumby focuses on "elementary" fast algorithms in sums of two and four squares. The actual talk had been accompanied by dazzling computer demonstrations. The detailed review of H. Cohn describes the construction of modular equations as the basis of studies of modular forms in the one-dimensional and Hilbert cases.
List of contents
1 Sums of Four Squares.- 2 On the Number of Co-Prime-Free Sets.- 3 The Primary Role of Modular Equations.- 4 Approximation Methods in Transcendental Function Computations and Some Physical Applications.- 5 Diophantine Approximation Problem Arising From VLSI Design.- 6 Linear Diophantine Problems.- 7 On the Sum of the Reciprocals of the Differences Between Consecutive Primes.- 8 The Smallest Maximal Set of Pairwise Disjoint Partitions.- 9 Sum Set Cardinalities of Line Restricted Planar Sets.- 10 On Solvability of a System of Two Boolean Linear Equations.- 11 Brauer Number and Twisted Fermat Motives.- 12 A Remark on a Paper of Erdös and Nathanson.- 13 Towards a Classification of Hilbert Modular Threefolds.- 14 Special Theta Relations.- 15 Minimal Bases and g-adic Representations of Integers.- 16 Finite Graphs and the Number of Sums and Products.- 17 Hilbert's Theorem 94 and Function Fields.- 18 Some Applications of Probability to Additive Number Theory and Harmonic Analysis.- 19 Quadratic Irrationals and Continued Fractions.- 20 Progression Bases for Finite Cyclic Groups.- 21 Sums of Finite Sets.- 22 Four Squares with Few Squares.
Summary
This volume is dedicated to Harvey Cohn, Distinguished Professor Emeritus of Mathematics at City College (CUNY). Harvey was one of the organizers of the New York Number Theory Seminar, and was deeply involved in all aspects of the Seminar from its first meeting in January, 1982, until his retirement in December, 1995. We wish him good health and continued hapiness and success in mathematics. The papers in this volume are revised and expanded versions of lectures delivered in the New York Number Theory Seminar. The Seminar meets weekly at the Graduate School and University Center of the City University of New York (CUNY). In addition, some of the papers in this book were presented at a conference on Combinatorial Number Theory that the New York Number Theory Seminar organized at Lehman College (CUNY). Here is a short description of the papers in this volume. The paper of R. T. Bumby focuses on "elementary" fast algorithms in sums of two and four squares. The actual talk had been accompanied by dazzling computer demonstrations. The detailed review of H. Cohn describes the construction of modular equations as the basis of studies of modular forms in the one-dimensional and Hilbert cases.
