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Transcendence in Algebra, Combinatorics, Geometry and Number Theory

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Cover of 'Transcendence in Algebra, Combinatorics, Geometry and Number Theory'

Table of Contents

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    Book Overview
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    Chapter 1 Frobenius Action on a Hypergeometric Curve and an Algorithm for Computing Values of Dwork’s p -adic Hypergeometric Functions
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    Chapter 2 A Matrix Version of Dwork’s Congruences
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    Chapter 3 On the Kernel Curves Associated with Walks in the Quarter Plane
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    Chapter 4 A Survey on the Hypertranscendence of the Solutions of the Schröder’s, Böttcher’s and Abel’s Equations
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    Chapter 5 Hodge Structures and Differential Operators
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    Chapter 6 Beck-Type Identities for Euler Pairs of Order r
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    Chapter 7 Quarter-Plane Lattice Paths with Interacting Boundaries: The Kreweras and Reverse Kreweras Models
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    Chapter 9 A Theta Identity of Gauss Connecting Functions from Additive and Multiplicative Number Theory
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    Chapter 10 Combinatorial Quantum Field Theory and the Jacobian Conjecture
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    Chapter 12 Néron Desingularization of Extensions of Valuation Rings
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    Chapter 14 Proof of Chudnovskys’ Hypergeometric Series for $$1/\pi $$ 1 / π Using Weber Modular Polynomials
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    Chapter 15 Computing an Order-Complete Basis for $$M^{\infty }(N)$$ M ∞ ( N ) and Applications
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    Chapter 16 An Algorithm to Prove Holonomic Differential Equations for Modular Forms
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    Chapter 17 A Case Study for $$\zeta (4)$$ ζ ( 4 )
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    Chapter 18 Support of an Algebraic Series as the Range of a Recursive Sequence
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    Chapter 19 X -coordinates of Pell Equations in Various Sequences
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    Chapter 20 A Conditional Proof of the Leopoldt Conjecture for CM Fields
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    Chapter 21 Siegel’s Problem for E -Functions of Order 2
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    Chapter 22 Irrationality and Transcendence of Alternating Series via Continued Fractions
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    Chapter 23 On the Transcendence of Critical Hecke L -Values
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Title
Transcendence in Algebra, Combinatorics, Geometry and Number Theory
Published by
Springer International Publishing, January 2021
DOI 10.1007/978-3-030-84304-5
ISBNs
978-3-03-084303-8, 978-3-03-084304-5
Editors

Bostan, Alin, Raschel, Kilian

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