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1.

図書

図書
Takeyuki Hida and Si Si
出版情報: Singapore : World Scientific, c2004  xiii, 189 p. ; 24 cm
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2.

図書

図書
[edited by] Lennart Berggren, Jonathan Borwein, Peter Borwein
出版情報: New York ; Tokyo : Springer, c2004  xix, 797 p. ; 26cm
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3.

図書

図書
edited by M. Delgado, J. López-Gómez, R. Ortega, A Suárez
出版情報: Singapore : World Scientific, c2004  xii, 246 p. ; 24 cm
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4.

図書

図書
[Nicole Berline and Claude Sabbah, comité éditorial]
出版情報: Palaiseau [France] : Editions de l'Ecole polytechnique, c2004  v, 95 p. ; 24 cm
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目次情報:
Un peu d'histoire des groupes finis et quelques exemples simples / Anne-Marie Aubert
Sur quelques groupes simples sporadiques / Michel Broué
Calculs en théorie des groupes : introduction au logiciel GAP (Groups, Algorithms, Programming) /Jean Michel
Un peu d'histoire des groupes finis et quelques exemples simples / Anne-Marie Aubert
Sur quelques groupes simples sporadiques / Michel Broué
Calculs en théorie des groupes : introduction au logiciel GAP (Groups, Algorithms, Programming) /Jean Michel
5.

図書

図書
edited by Oliver Roth and Stephan Ruscheweyh
出版情報: Lemgo : Heldermann Verlag, c2004  l, 480 p. ; 25 cm
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6.

図書

図書
Colin C. Adams
出版情報: Providence, R.I. : American Mathematical Society, c2004  xiii, 306 p. ; 26 cm
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目次情報: 続きを見る
Introduction
Tabulating knots Invariants of knots Surfaces and knots
Types of knots Polynomials Biology, chemistry, and physics Knots, links, and graphs
Topology Higher dimensional knotting Knot jokes and pastimes
Appendix
Suggested readings and references
Index Corrections to the 2004 AMS printing
Introduction
Tabulating knots Invariants of knots Surfaces and knots
Types of knots Polynomials Biology, chemistry, and physics Knots, links, and graphs
7.

図書

図書
by Dinesh S. Thakur
出版情報: Singapore : World Scientific, c2004  xv, 388 p. ; 24 cm
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目次情報: 続きを見る
Number fields and Function fields / 1:
Global fields: Basic analogies and contrasts / 1.1:
Genus and Riemann-Roch theorem / 1.2:
Zeta function and class group / 1.3:
Class field theory and Galois group / 1.4:
Drinfeld modules / 2:
Carlitz module and related arithmetical objects / 2.1:
Drinfeld modules: Basic definitions / 2.2:
Torsion points / 2.3:
Analytic theory / 2.4:
Explicit calculations for Carlitz module / 2.5:
Reductions / 2.6:
Endomorphisms / 2.7:
Field of definition / 2.8:
Points on Drinfeld modules / 2.9:
Adjoints and duality / 2.10:
Useful tools in non-archimedean or finite field setting / 2.11:
Properties of k{[tau]} / (a):
Moore determinant / (b):
q-resultants / (c):
Non-archimedean calculus / (d):
Dwork's trace formula / (e):
Explicit class field theory / 3:
Torsion of rank one Drinfeld modules / 3.1:
Sign normalization of the top coefficient / 3.2:
Normalizing Field as a class field / 3.3:
Smallest field of definition as a class field / 3.4:
Ring of definition / 3.5:
Cyclotomic fields / 3.6:
Moduli approach / 3.7:
Summary / 3.8:
Maximal abelian extension / 3.9:
Cyclotomic theory of F[subscript q t] / 3.10:
Cyclotomic units and conjectures of Brumer and Stark / 3.11:
Some contrasts and open questions / 3.12:
Gauss sums and Gamma functions / 4:
Gauss and Jacobi sums: Definitions / 4.1:
Gauss and Jacobi sums: F[subscript q t] case / 4.2:
Gauss and Jacobi sums: General A / 4.3:
Sign of Gauss sums for F[subscript q t] / 4.4:
Arithmetic Factorial and Gamma: Definitions / 4.5:
F[subscript q t] case
General A
Functional equations in arithmetic case / 4.6:
Special values for arithmetic [Gamma subscript infinity] / 4.7:
Periods: F[subscript q t] case
Periods: General A
Special values of arithmetic [Gamma subscript v] / 4.8:
F[subscript q t] case: Analog of Gross-Koblitz
Geometric Factorial and Gamma: Definitions / 4.9:
Functional equations in geometric case / 4.10:
Special values of geometric [Gamma] and [Gamma subscript v]: F[subscript q t] case / 4.11:
Comparisons and uniform framework / 4.12:
More analogies for F[subscript q t]: Divisibilities / 4.13:
Binomial coefficients / 4.14:
Binomial coefficients as nice basis
Difference and differentiation operators
Relations between the two notions of binomials / 4.15:
Bernoulli numbers and polynomials / 4.16:
Note on finite differences and q-analogs / 4.17:
Zeta functions / 5:
Zeta values at integers: Definitions / 5.1:
Values at positive integers / 5.2:
Values at non-positive integers / 5.3:
Multiplicities of trivial zeros / 5.4:
Zeta function interpolation on character space / 5.5:
[infinity]-adic interpolation
p adic interpolation
Power sums / 5.6:
Zeta measure / 5.7:
Zero distribution / 5.8:
Low values and multi-logarithms / 5.9:
Multizeta values / 5.10:
Complex valued multizeta
Finite characteristic variants
Interpolations
Analytic properties of zeta and Fredholm determinant / 5.11:
Note on classical interpolations / 5.12:
Higher rank theory / 6:
Elliptic modules / 6.1:
Modular forms / 6.2:
Galois representations / 6.3:
DeRham Cohomology / 6.4:
Elliptic curves case: Motivation
Drinfeld modules case
Hypergeometric functions / 6.5:
The first analog
The second analog
Higher dimensions and geometric tools / 7:
t-modules and t-motives / 7.1:
Torsion / 7.2:
Purity / 7.3:
Exponential, period lattice and uniformizability / 7.4:
Cohomology realizations / 7.5:
Example: Carlitz-Tate twist C[superscript multiply sign in circle n] / 7.6:
Drinfeld dictionary in the simplest case / 7.7:
Krichever/Drinfeld dictionary in more generality / 7.8:
Applications to Gauss sums, Gamma and Zeta values / 8:
C[superscript multiply sign in circle n] and [xi](n) / 8.1:
Shtuka and Jacobi sums / 8.2:
Gauss sums and Theta divisor
Examples and applications
The case g = d[subscript infinity] = 1
Another Gamma function / 8.3:
Analog of Gross-Koblitz
Interpolation at [infinity] for new Gamma
Fermat motives and Solitons / 8.4:
Another approach to solitons / 8.5:
Analog of Gross-Koblitz for Geometric Gamma: F[subscript q t] case / 8.6:
What is known or expected in general case? / 8.7:
Gamma values to Periods connection via solitons: Sketch / 8.8:
Log-algebraicity, Cyclotomic module and Vandiver conjecture / 8.9:
Explicit Log-Algebraicity formulas / 8.10:
Diophantine approximation / 9:
Approximation exponents / 9.1:
Good approximations: Continued fractions / 9.2:
Range of exponents: Frobenius / 9.3:
Range of exponents: Differentiation / 9.4:
Connection with deformation theory / 9.5:
Height inequalities for algebraic points
Exponent hierarchy
Approximation by algebraic functions
Note on connection with Diophantine equations / 9.6:
Transcendence results / 10:
Approximation techniques and irrationality / 10.1:
Transcendence results on Drinfeld modules / 10.2:
Application to Zeta and Gamma values / 10.3:
Transcendence results in higher dimensions / 10.4:
Automata and algebraicity: Applications / 10.5:
Automata and algebraicity / 11.1:
Some useful automata tools / 11.2:
Applications to transcendence of gamma values and monomials / 11.3:
Applications to transcendence: periods and modular functions / 11.4:
Classifying finite characteristic numbers / 11.5:
Computational classes and basic tools / 11.6:
Algebraic properties of computational classes / 11.7:
Applications to refined transcendence / 11.8:
Note on the Notation
Bibliography
Number fields and Function fields / 1:
Global fields: Basic analogies and contrasts / 1.1:
Genus and Riemann-Roch theorem / 1.2:
8.

図書

図書
edited by Vladimir I. Arnold
出版情報: Berlin ; Tokyo : Springer, c2004  xiv, 639 p. ; 24 cm
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9.

図書

図書
Marc Nieper-Wißkirchen
出版情報: River Edge, NJ : World Scientific, c2004  xxii, 150 p. ; 24 cm
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10.

図書

図書
Fritz Keinert
出版情報: Boca Raton : Chapman & Hall/CRC, c2004  xii, 275 p. ; 25 cm
シリーズ名: Studies in advanced mathematics
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