Number Theory and Related Fields

1. Front Matter

   Pages i-x

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2. Life and Mathematics of Alfred Jacobus van der Poorten (1942–2010)

   • David Hunt

   Pages 1-53

3. Ramanujan–Sato-Like Series

   • Gert Almkvist, Jesús Guillera

   Pages 55-74

4. On the Sign of the Real Part of the Riemann Zeta Function

   • Juan Arias de Reyna, Richard P. Brent, Jan van de Lune

   Pages 75-97

5. Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition

   • Khodakhast Bibak

   Pages 99-128

6. Transcendence of Stammering Continued Fractions

   • Yann Bugeaud

   Pages 129-141

7. Algebraic Independence of Infinite Products and Their Derivatives

   • Peter Bundschuh

   Pages 143-156

8. Small Representations by Indefinite Ternary Quadratic Forms

   • J. B. Friedlander, H. Iwaniec

   Pages 157-164

9. Congruences for Andrews’ spt-Function Modulo 32760 and Extension of Atkin’s Hecke-Type Partition Congruences

   • F. G. Garvan

   Pages 165-185

10. Continued Fractions and Dedekind Sums for Function Fields

    • Yoshinori Hamahata

    Pages 187-197

11. Burgess’s Bounds for Character Sums

    • D. R. Heath-Brown

    Pages 199-213

12. Structured Hadamard Conjecture

    • Ilias S. Kotsireas

    Pages 215-227

13. Families of Cubic Thue Equations with Effective Bounds for the Solutions

    • Claude Levesque, Michel Waldschmidt

    Pages 229-243

14. Consequences of a Factorization Theorem for Generalized Exponential Polynomials with Infinitely Many Integer Zeros

    • Ouamporn Phuksuwan, Vichian Laohakosol

    Pages 245-252

15. On Balanced Subgroups of the Multiplicative Group

    • Carl Pomerance, Douglas Ulmer

    Pages 253-270

16. Some Extensions of the Lucas Functions

    • E. L. Roettger, H. C. Williams, R. K. Guy

    Pages 271-311

17. The Impact of Number Theory and Computer-Aided Mathematics on Solving the Hadamard Matrix Conjecture

    • Jennifer Seberry

    Pages 313-320

18. Description of Generalized Continued Fractions by Finite Automata

    • Jeffrey Shallit

    Pages 321-339

19. On Prime Factors of Terms of Linear Recurrence Sequences

    • C. L. Stewart

    Pages 341-359

20. Some Notes on Weighted Sum Formulae for Double Zeta Values

    • James Wan

    Pages 361-379

“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.​  

• number theory

• , School of Math. & Physical Sciences, University of Newcastle, Callaghan, Australia

  Jonathan M. Borwein, Wadim Zudilin

• , Department of Computing, Macquarie University, North Ryde, Australia

  Igor Shparlinski

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