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Transcendence in Algebra, Combinatorics, Geometry and Number Theory

TRANS19 – Transient Transcendence in Transylvania, Brașov, Romania, May 13–17, 2019, Revised and Extended Contributions

  • Conference proceedings
  • © 2021

Overview

Editors:
  1. Alin Bostan

    1. Inria, Université Paris-Saclay, Palaiseau, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Kilian Raschel

    1. CNRS, Institut Denis Poisson, Université de Tours,, Tours, France

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Brings original articles on algebraic and transcendental aspects of special functions and special numbers
  • Highlights collaboration in number theory, combinatorics, statistical mechanics, and computer algebra
  • Offers selected surveys on key topics in these fields

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 373)

Included in the following conference series:

Conference proceedings info: TRANS 2019.

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Table of contents (23 papers)

  1. Front Matter

    Pages i-xxxix
    Download chapter PDF

  2. Frobenius Action on a Hypergeometric Curve and an Algorithm for Computing Values of Dwork’s p-adic Hypergeometric Functions

    • Masanori Asakura
    Pages 1-45

  3. A Matrix Version of Dwork’s Congruences

    • Frits Beukers
    Pages 47-59

  4. On the Kernel Curves Associated with Walks in the Quarter Plane

    • Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael F. Singer
    Pages 61-89

  5. A Survey on the Hypertranscendence of the Solutions of the Schröder’s, Böttcher’s and Abel’s Equations

    • Gwladys Fernandes
    Pages 91-125

  6. Hodge Structures and Differential Operators

    • Masha Vlasenko
    Pages 127-139

  7. Beck-Type Identities for Euler Pairs of Order r

    • Cristina Ballantine, Amanda Welch
    Pages 141-161

  8. Quarter-Plane Lattice Paths with Interacting Boundaries: The Kreweras and Reverse Kreweras Models

    • Nicholas R. Beaton, Aleksander L. Owczarek, Ruijie Xu
    Pages 163-192

  9. Infinite Product Formulae for Generating Functions for Sequences of Squares

    • Christian Krattenthaler, Mircea Merca, Cristian-Silviu Radu
    Pages 193-236

  10. A Theta Identity of Gauss Connecting Functions from Additive and Multiplicative Number Theory

    • Mircea Merca
    Pages 237-248

  11. Combinatorial Quantum Field Theory and the Jacobian Conjecture

    • A. Tanasa
    Pages 249-259

  12. How Regular are Regular Singularities?

    • Herwig Hauser
    Pages 261-273

  13. Néron Desingularization of Extensions of Valuation Rings

    • Dorin Popescu
    Pages 275-307

  14. Diagonal Representation of Algebraic Power Series: A Glimpse Behind the Scenes

    • Sergey Yurkevich
    Pages 309-339

  15. Proof of Chudnovskys’ Hypergeometric Series for \(1/\pi \) Using Weber Modular Polynomials

    • Jesús Guillera
    Pages 341-354

  16. Computing an Order-Complete Basis for \(M^{\infty }(N)\) and Applications

    • Mark van Hoeij, Cristian-Silviu Radu
    Pages 355-366

  17. An Algorithm to Prove Holonomic Differential Equations for Modular Forms

    • Peter Paule, Cristian-Silviu Radu
    Pages 367-420

  18. A Case Study for \(\zeta (4)\)

    • Carsten Schneider, Wadim Zudilin
    Pages 421-435

  19. Support of an Algebraic Series as the Range of a Recursive Sequence

    • Jason P. Bell
    Pages 437-449

  20. X-coordinates of Pell Equations in Various Sequences

    • Florian Luca
    Pages 451-463
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Other volumes

  1. Transcendence in Algebra, Combinatorics, Geometry and Number Theory

Keywords

About this book

This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.

Editors and Affiliations

  • Inria, Université Paris-Saclay, Palaiseau, France

    Alin Bostan

  • CNRS, Institut Denis Poisson, Université de Tours,, Tours, France

    Kilian Raschel

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