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Algebraic Number Theory and Diophantine Analysis: Proceedings of the International Conference Held in Graz, Austria, August 30 to September 5, 1998

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Most of the 35 papers presented at the September 1998 conference discuss algebraic number theory, diophantine and algorithmic problems, diophantine equations, uniform distribution, and discrepancy theory. Topics include small values of diagonal cubic forms, galois module structure for wild extensions, the class number one problem for the dihedral CM-fields, factorization in some orders with a PID as integral closure, and representation of large integers as sums of two primes of special type. No index. Annotation c. Book News, Inc., Portland, OR (
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Product Details

Table of Contents

Preface v
List of participants xi
Monochromatic solutions of Diophantine equations 1
Cubic Pisot units with finite beta expansions 11
Small values of diagonal cubic forms 27
On the approximation by algebraic numbers with bounded degree 47
Galois module structure and Kummer theory for Lubin--Tate formal groups 55
Galois module structure for wild extensions 69
Multiplicative dependence and bounded height, an example 93
The distribution of patterns in digital expansions 103
A note on Diophantine quintuples 123
Symmetric improvements of Liouville's inequality: A survey 129
On the distribution of the sums of binomial coefficients modulo a prime 143
Computing power integral bases in algebraic number fields II 153
Cuspidal divisor class groups of modular curves 163
Discriminant form and index form equations 191
On general families of parametrized Thue equations 215
Computing elliptic curves having good reduction everywhere over quadratic fields II 239
The class number one problem for the dihedral CM-fields 249
On Tate--Shafarevich groups of some elliptic curves 277
Polylogarithms and arithmetic functions 293
On the diophantine equation (x[superscript n] - 1)/(x - 1) = y[superscript q] 305
Distribution of Kronecker sequences 311
Finite polynomial orbits. A survey 331
Diophantine approximation in R[superscript s]: On a method of Mordell and Armitage 339
S-integer points on elliptic curves, theory and practice 351
Factorization in some orders with a PID as integral closure 365
Topologies induced by systems of divisors 391
Hartman and Beatty bisequences 405
Moment problem of the type [function of superscript 1 subscript 0] [function of superscript 1 subscript 0] F(x, y)dg(x)dg(y) = 0 423
Conner's Level Condition 445
Remarks on Iwasawa [lambda]-invariants 453
Exact covers of balanced sequences and Fraenkel's conjecture 467
Representations of large integers as sums of two primes of special type 485
Conjectures for large transcendence degree 497
On Lambert's proof of the irrationality of [pi] 521
Diophantine equations of the form aX[superscript 4] - bY[superscript 2] = [plus or minus]1 531
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