Ebook: Number Theory and Related Fields: In Memory of Alf van der Poorten

“Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.​

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Number Theory and Related Fields collects contributions based on the proceedings of the “International Number Theory Conference in Memory of Alf van der Poorten,” hosted by CARMA and held March 12–16, 2012, at the University of Newcastle, Australia. The purpose of the conference was to commemorate the research and influence of Alf van der Poorten in number theory and in general mathematics and presented an exciting venue for promoting number-theoretic research and graduate study in Australia. Comprehensive accounts of recent achievements in theoretical and computational number theory and its applications to cryptography and theoretical computer science were also paramount to the conference.

The volume begins with a detailed academic appreciation of van der Poorten’s life and work, and includes research articles written by some of the most distinguished mathematicians in the field of number theory. Contributions also include related topics that focus on the various research interests of van der Poorten, such as continued fractions and elliptic curves. Researchers in number theory and its applications will find this Proceedings of great interest.

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Number Theory and Related Fields collects contributions based on the proceedings of the “International Number Theory Conference in Memory of Alf van der Poorten,” hosted by CARMA and held March 12–16, 2012, at the University of Newcastle, Australia. The purpose of the conference was to commemorate the research and influence of Alf van der Poorten in number theory and in general mathematics and presented an exciting venue for promoting number-theoretic research and graduate study in Australia. Comprehensive accounts of recent achievements in theoretical and computational number theory and its applications to cryptography and theoretical computer science were also paramount to the conference.

The volume begins with a detailed academic appreciation of van der Poorten’s life and work, and includes research articles written by some of the most distinguished mathematicians in the field of number theory. Contributions also include related topics that focus on the various research interests of van der Poorten, such as continued fractions and elliptic curves. Researchers in number theory and its applications will find this Proceedings of great interest.

Content:
Front Matter....Pages i-x
Life and Mathematics of Alfred Jacobus van der Poorten (1942–2010)....Pages 1-53
Ramanujan–Sato-Like Series....Pages 55-74
On the Sign of the Real Part of the Riemann Zeta Function....Pages 75-97
Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition....Pages 99-128
Transcendence of Stammering Continued Fractions....Pages 129-141
Algebraic Independence of Infinite Products and Their Derivatives....Pages 143-156
Small Representations by Indefinite Ternary Quadratic Forms....Pages 157-164
Congruences for Andrews’ spt-Function Modulo 32760 and Extension of Atkin’s Hecke-Type Partition Congruences....Pages 165-185
Continued Fractions and Dedekind Sums for Function Fields....Pages 187-197
Burgess’s Bounds for Character Sums....Pages 199-213
Structured Hadamard Conjecture....Pages 215-227
Families of Cubic Thue Equations with Effective Bounds for the Solutions....Pages 229-243
Consequences of a Factorization Theorem for Generalized Exponential Polynomials with Infinitely Many Integer Zeros....Pages 245-252
On Balanced Subgroups of the Multiplicative Group....Pages 253-270
Some Extensions of the Lucas Functions....Pages 271-311
The Impact of Number Theory and Computer-Aided Mathematics on Solving the Hadamard Matrix Conjecture....Pages 313-320
Description of Generalized Continued Fractions by Finite Automata....Pages 321-339
On Prime Factors of Terms of Linear Recurrence Sequences....Pages 341-359
Some Notes on Weighted Sum Formulae for Double Zeta Values....Pages 361-379
Period(d)ness of L-Values....Pages 381-395

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Number Theory and Related Fields collects contributions based on the proceedings of the “International Number Theory Conference in Memory of Alf van der Poorten,” hosted by CARMA and held March 12–16, 2012, at the University of Newcastle, Australia. The purpose of the conference was to commemorate the research and influence of Alf van der Poorten in number theory and in general mathematics and presented an exciting venue for promoting number-theoretic research and graduate study in Australia. Comprehensive accounts of recent achievements in theoretical and computational number theory and its applications to cryptography and theoretical computer science were also paramount to the conference.

The volume begins with a detailed academic appreciation of van der Poorten’s life and work, and includes research articles written by some of the most distinguished mathematicians in the field of number theory. Contributions also include related topics that focus on the various research interests of van der Poorten, such as continued fractions and elliptic curves. Researchers in number theory and its applications will find this Proceedings of great interest.

Content:
Front Matter....Pages i-x
Life and Mathematics of Alfred Jacobus van der Poorten (1942–2010)....Pages 1-53
Ramanujan–Sato-Like Series....Pages 55-74
On the Sign of the Real Part of the Riemann Zeta Function....Pages 75-97
Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition....Pages 99-128
Transcendence of Stammering Continued Fractions....Pages 129-141
Algebraic Independence of Infinite Products and Their Derivatives....Pages 143-156
Small Representations by Indefinite Ternary Quadratic Forms....Pages 157-164
Congruences for Andrews’ spt-Function Modulo 32760 and Extension of Atkin’s Hecke-Type Partition Congruences....Pages 165-185
Continued Fractions and Dedekind Sums for Function Fields....Pages 187-197
Burgess’s Bounds for Character Sums....Pages 199-213
Structured Hadamard Conjecture....Pages 215-227
Families of Cubic Thue Equations with Effective Bounds for the Solutions....Pages 229-243
Consequences of a Factorization Theorem for Generalized Exponential Polynomials with Infinitely Many Integer Zeros....Pages 245-252
On Balanced Subgroups of the Multiplicative Group....Pages 253-270
Some Extensions of the Lucas Functions....Pages 271-311
The Impact of Number Theory and Computer-Aided Mathematics on Solving the Hadamard Matrix Conjecture....Pages 313-320
Description of Generalized Continued Fractions by Finite Automata....Pages 321-339
On Prime Factors of Terms of Linear Recurrence Sequences....Pages 341-359
Some Notes on Weighted Sum Formulae for Double Zeta Values....Pages 361-379
Period(d)ness of L-Values....Pages 381-395
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