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Directions in Number Theory

Proceedings of the 2014 WIN3 Workshop

  • Conference proceedings
  • © 2016

Overview

Editors:
  1. Ellen E. Eischen

    1. Department of Mathematics, University of Oregon, Eugene, USA

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  2. Ling Long

    1. Department of Mathematics, Louisiana State University, Baton Rouge, USA

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  3. Rachel Pries

    1. Department of Mathematics, Colorado State University, Fort Collins, USA

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  4. Katherine E. Stange

    1. Department of Mathematics, University of Colorado, Boulder, USA

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  • Includes papers spanning a wide range of research areas, including arithmetic geometry, analytic number theory, algebraic number theory, and applications to coding and cryptography
  • Features the contributions of over 40 number theorists, stemming from collaborations between senior and mid-level faculty, junior faculty and postdocs, and graduate students
  • Presents a compilation of research and survey papers
  • Includes supplementary material: sn.pub/extras

Part of the book series: Association for Women in Mathematics Series (AWMS, volume 3)

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Table of contents (10 papers)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Insufficiency of the Brauer–Manin Obstruction for Rational Points on Enriques Surfaces

    • Francesca Balestrieri, Jennifer Berg, Michelle Manes, Jennifer Park, Bianca Viray
    Pages 1-31

  3. Shadow Lines in the Arithmetic of Elliptic Curves

    • J. S. Balakrishnan, M. Çiperiani, J. Lang, B. Mirza, R. Newton
    Pages 33-55

  4. Galois Action on the Homology of Fermat Curves

    • Rachel Davis, Rachel Pries, Vesna Stojanoska, Kirsten Wickelgren
    Pages 57-86

  5. Zeta Functions of a Class of Artin–Schreier Curves with Many Automorphisms

    • Irene Bouw, Wei Ho, Beth Malmskog, Renate Scheidler, Padmavathi Srinivasan, Christelle Vincent
    Pages 87-124

  6. Hypergeometric Series, Truncated Hypergeometric Series, and Gaussian Hypergeometric Functions

    • Alyson Deines, Jenny G. Fuselier, Ling Long, Holly Swisher, Fang-Ting Tu
    Pages 125-159

  7. A Generalization of S. Zhang’s Local Gross–Zagier Formula for GL2

    • Kathrin Maurischat
    Pages 161-196

  8. p-Adic q-Expansion Principles on Unitary Shimura Varieties

    • Ana Caraiani, Ellen Eischen, Jessica Fintzen, Elena Mantovan, Ila Varma
    Pages 197-243

  9. Kneser–Hecke-Operators for Codes over Finite Chain Rings

    • Amy Feaver, Anna Haensch, Jingbo Liu, Gabriele Nebe
    Pages 245-270

  10. Ring-LWE Cryptography for the Number Theorist

    • Yara Elias, Kristin E. Lauter, Ekin Ozman, Katherine E. Stange
    Pages 271-290

  11. Asymptotics for Number Fields and Class Groups

    • Melanie Matchett Wood
    Pages 291-339
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Keywords

About this book

Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014. The papers span a wide range of research areas: arithmetic geometry; analytic number theory; algebraic number theory; and applications to coding and cryptography.


The WIN conference series began in 2008, with the aim of strengthening the research careers of female number theorists. The series introduced a novel research-mentorship model: women at all career stages, from graduate students to senior members of the community, joined forces to work in focused research groups on cutting-edge projects designed and led by experienced researchers. The goals for Women In Numbers 3 were to establish ambitious new collaborations between women in number theory, to train junior participants about topics of current importance, and to continue to build a vibrant community of women in number theory. Forty-two women attended the WIN3 workshop, including 15 senior and mid-level faculty, 15 junior faculty and postdocs, and 12 graduate students.

Editors and Affiliations

  • Department of Mathematics, University of Oregon, Eugene, USA

    Ellen E. Eischen

  • Department of Mathematics, Louisiana State University, Baton Rouge, USA

    Ling Long

  • Department of Mathematics, Colorado State University, Fort Collins, USA

    Rachel Pries

  • Department of Mathematics, University of Colorado, Boulder, USA

    Katherine E. Stange

Bibliographic Information

  • Book Title: Directions in Number Theory

  • Book Subtitle: Proceedings of the 2014 WIN3 Workshop

  • Editors: Ellen E. Eischen, Ling Long, Rachel Pries, Katherine E. Stange

  • Series Title: Association for Women in Mathematics Series

  • DOI: https://doi.org/10.1007/978-3-319-30976-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2016

  • Hardcover ISBN: 978-3-319-30974-3Published: 27 September 2016

  • Softcover ISBN: 978-3-319-80934-2Published: 14 June 2018

  • eBook ISBN: 978-3-319-30976-7Published: 26 September 2016

  • Series ISSN: 2364-5733

  • Series E-ISSN: 2364-5741

  • Edition Number: 1

  • Number of Pages: XV, 339

  • Number of Illustrations: 12 b/w illustrations, 1 illustrations in colour

  • Topics: Number Theory, Topological Groups, Lie Groups, Geometry

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