Number Theory
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Edited by:
Matti Jutila
About this book
These Proceedings contain 22 refereed research and survey articles based on lectures given at the Turku Symposium on Number Theory in Memory of Kustaa Inkeri, held in Turku, Finland, from May 31 to June 4, 1999. The subject of the symposium was number theory in a broad sense with an emphasis on recent advances and modern methods. The topics covered in this volume include various questions in elementary number theory, new developments in classical Diophantine problems - in particular of the Fermat and Catalan type, the ABC-conjecture, arithmetic algebraic geometry, elliptic curves, Diophantine approximations, Abelian fields, exponential sums, sieve methods, box splines, the Riemann zeta-function and other Dirichlet series, and the spectral theory of automorphic functions with its arithmetical applications.
Author / Editor information
Professor Matti Jutila, Professor Tauno Metsänkylä, Department of Mathematics, University of Turku, Finland.
Topics
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Frontmatter
I -
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Preface
V -
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Table of Contents
VII -
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On the life and work of Kustaa Inkeri
1 -
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On the values of certain q-hypergeometric series
5 -
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On the Diophantine equation
19 -
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Arithmetical properties of the solutions of certain functional equations
25 -
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Multiple zeta sums via box splines
43 -
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Galois representations attached to elliptic curves and diophantine problems
71 -
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One-sided sifting density hypotheses in Selberg's sieve
105 -
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On characterizations of completely multiplicative arithmetical functions
115 -
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A note on the power residue symbol
125 -
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Exponential sums with a large second derivative
131 -
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Some mean value results for the Riemann zeta-function
145 -
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Direct proofs of some of Euler's results
163 -
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The fourth moment of central values of Hecke series
167 -
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The universality of Dirichlet series attached to finite Abelian groups
179 -
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An irrationality criterion for p-adic binomial series
193 -
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The mean values and the universality of Rankin-Selberg L-functions
201 -
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On the binary additive divisor problem
223 -
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Catalan's equation just before 2000
247 -
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New analytic problems over imaginary quadratic number fields
255 -
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On number theory and Kustaa Inkeri
281 -
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On Lucas sequence terms of the form kx2
293 -
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Stark's question and Popescu's conjecture for abelian L-functions
305 -
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Partial Pell numbers
317 -
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List of participants
323
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