Automorphic Forms

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.

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

Inhalt
Preface.- On formal series of Jacobi forms and Borcherds products.- Finite or Infinite Number of Solutions of Polynomial Congruences in two Positive Integer Variables.- On the genus version of the basis problem II: The case of oldforms.- Restrictions of Jacobi Forms of Several Variables with special emphasis on Quaternionic Jacobi Forms.- Additive and multiplicative lifting properties of the Igusa modular form.- On the special values of certain L-series related to half-integral weight modular forms.- On explicit dimension formulas for spaces of Siegel cusp forms of degree two and their applications.- Borcherds lift on the paramodular group of level 3.- On the proportion of quadratic twists for non-vanishing and vanishing central values of L-functions attached to primitive forms.- On the Existence of Hermitian Self-Dual Extended Abelian Group Codes.- On p-adic properties of Siegel modular forms.- Bessel periods of theta lifts to GSp(1,1) and central values of some L-functions of convolution type.- Intersections of two walls of the Gottschling fundamental domain of the Siegel modular group of genus two.- Non-vanishing of L-functions associated to cusp forms of half-integral weight.- The Restriction of Octonionic Theta Constants to the Quaternionic Half-space.- Hermitian modular forms of degree 2 over the Eisenstein integers.