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Automorphic Forms

Research in Number Theory from Oman

  • Conference proceedings
  • © 2014

Overview

Editors:
  1. Bernhard Heim

    1. Department of Mathematics and Science, German University of Technology in Oman, Muscat, Oman

  2. Mehiddin Al-Baali

    1. Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman

  3. Tomoyoshi Ibukiyama

    1. Department of Mathematics Graduate School of Science, Osaka University, Osaka, Japan

  4. Florian Rupp

    1. Department of Mathematics and Science, German University of Technology in Oman, Muscat, Oman

  • Presents research on number theory and automorphic forms presented at the Inaugural Conference on Modern Number Theory and Its Applications at German University of Technology in Oman in February 2012
  • Brings together the work of students, postdocs and experts in the field of modern number theory, providing a platform for scientific exchange and to build a bridge between scientists from Germany, Japan, and Oman
  • Includes surveys, outlines of research projects and genuine research articles presented at the conference on topics including Borcherds products, congruences and codes, Jacobi forms, Siegel and Hermitian modular forms, and special values of L-series
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 115)

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About this book

This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 “International Conference on Automorphic Forms and Number Theory,” held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of:

  • Borcherds products
  • Congruences and Codes
  • Jacobi forms
  • Siegel and Hermitian modular forms
  • Special values of L-series

Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and Japan. The conference was hosted by the Sultan Qaboos University and the German University of Technology in Oman.

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Table of contents (17 papers)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. On Formal Series of Jacobi Forms and Borcherds Products

    • Hiroki Aoki
    Pages 1-10

  3. Finite or Infinite Number of Solutions of Polynomial Congruences in Two Positive Integer Variables

    • Thomas Bier
    Pages 11-26

  4. On the Genus Version of the Basis Problem II: The Case of Oldforms

    • Siegfried Böcherer
    Pages 27-46

  5. On p-Adic Properties of Siegel Modular Forms

    • Siegfried Böcherer, Shoyu Nagaoka
    Pages 47-66

  6. On the Existence of Hermitian Self-Dual Extended Abelian Group Codes

    • Lilibeth Dicuangco-Valdez, Pieter Moree, Patrick Solé
    Pages 67-84

  7. Restrictions of Jacobi Forms of Several Variables

    • Till Dieckmann
    Pages 85-92

  8. Reversing Borcherds Lifts: A Survey

    • Bernhard Heim, Atsushi Murase
    Pages 93-101

  9. Additive and Multiplicative Lifting Properties of the Igusa Modular Form

    • Bernhard Heim, Atsushi Murase
    Pages 103-117

  10. On the Special Values of Certain L-Series Related to Half-Integral Weight Modular Forms

    • Hidenori Katsurada
    Pages 119-136

  11. On Explicit Dimension Formulas for Spaces of Siegel Cusp Forms of Degree Two and Their Applications

    • Hidetaka Kitayama
    Pages 137-150

  12. Borcherds Lift on the Paramodular Group of Level 3

    • Judith Kreuzer
    Pages 151-161

  13. The Restriction of Octonionic Theta Constants to the Quaternionic Half-Space

    • C. Dieckmann, A. Krieg
    Pages 163-171

  14. On the Proportion of Quadratic Twists for Non-vanishing and Vanishing Central Values of L-Functions Attached to Primitive Forms

    • Kenji Makiyama
    Pages 173-178

  15. Bessel Periods of Theta Lifts to GSp(1, 1) and Central Values of Some L-Functions of Convolution Type

    • Hiro-aki Narita
    Pages 179-191

  16. Intersections of Two Walls of the Gottschling Fundamental Domain of the Siegel Modular Group of Genus Two

    • Takayuki Oda
    Pages 193-221

  17. Nonvanishing of L-Functions Associated to Cusp Forms of Half-Integral Weight

    • B. Ramakrishnan, Karam Deo Shankhadhar
    Pages 223-231

  18. Hermitian Modular Forms of Degree 2 over the Eisenstein Integers

    • Martin Woitalla
    Pages 233-242
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Editors and Affiliations

  • Department of Mathematics and Science, German University of Technology in Oman, Muscat, Oman

    Bernhard Heim, Florian Rupp

  • Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman

    Mehiddin Al-Baali

  • Department of Mathematics Graduate School of Science, Osaka University, Osaka, Japan

    Tomoyoshi Ibukiyama

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