Diophantine Analysis and Related Fields: Darf

These proceedings contain the papers presented at the DARF 2008 Conference as well as those papers presented at the DARF 2007 Conference which was held 7 - 9 March 2007 in Yokohama, Japan. The purpose of the conference was to report recent progress and developments of diophantine aspects of analytic number theory, especially focusing upon the topics in diophantine analysis and related fields; its simultaneous objectives are to promote interactions between analytic number theorists and mathematicians from other fields, and further to create opportunities for opening up new individual/collaborative research projects.

Preface	p. vii
List of Participants in 2007	p. ix
List of Contributed Speakers in 2008	p. xi
Conference Photo in 2007	p. xiii
Measure of Irrationality for Certain Infinite Series	p. 1
Irrationality via the Hypergeometric Method	p. 7
On a Mixed Littlewood Conjecture in Fields of Power Series	p. 19
Inhomogeneous Diophantine Approximation of Some Hurwitzian Numbers	p. 31
The Divided Cell Algorithm and the Inhomogeneous Lagrange and Markoff Spectra	p. 43
Conjectures and Results on the Size and Number of Diophantine Tuples	p. 58
On Series Involving Fibonacci and Lucas Numbers I	p. 62
Reciprocal Sums of Fibonacci Numbers	p. 77
Diophantine Quadruples Containing Some Triples and the Number of Diophantine Quintuples	p. 90
Dedekind Sums for Finite Fields	p. 96
Certain Integers Related to Ankeny-Artin-Chowla Conjecture	p. 103
Diophantine Approximation of the Values of Hypergeometric Function of Gauss	p. 106
Expansion of Real Numbers by Algebraic Numbers	p. 111
A Note on Poly-Bernoulli Numbers and Multiple Zeta Values	p. 118
A Note on Periodicity of p-adic Analytic Functions	p. 125
Leaping Convergents of Hurwitz Continued Fractions	p. 130
The Irrationality Criteria of Brun and Badea Are Essentially Equivalent	p. 144
On Approximation Measures of Certain q-continued Fractions	p. 160
On the Finiteness and Nonexistence of Certain mod 2 Galois Representations of Quadratic Fields	p. 169
On Exponential Sums of Digital Sums Related to Gelfond's Theorem	p. 176
Remarkable Algebraic Independence Property of Certain Series Related to Continued Fractions	p. 190
Recent Progress on Certain Quartic Diophantine Equations	p. 205
Author Index	p. 211
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Diophantine Analysis and Related Fields: Darf 2007/2008, DARF 2007, Yokohama, Japan 7-9 March 2007, DARF 2008, Kyoto, Japan 5-7 March 2008

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