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Integral Quadratic Forms and Lattices
Edited by: Myung-Hwan Kim, Seoul National University, Korea, John S. Hsia, Ohio State University, Columbus, OH, Yoshiyuki Kitaoka, Nagoya University, Japan, and Rainer Schulze-Pillot, Universität des Saarlandes, Saabrücken, Germany
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Contemporary Mathematics
1999; 302 pp; softcover
Volume: 249
ISBN-10: 0-8218-1949-6
ISBN-13: 978-0-8218-1949-4
List Price: US$110
Member Price: US$88
Order Code: CONM/249
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This volume presents the proceedings of an international conference held at Seoul National University (Korea). Talks covered recent developments in diverse areas related to the theory of integral quadratic forms and hermitian forms, local densities, linear relations and congruences of theta series, zeta functions of prehomogeneous vector spaces, lattices with maximal finite matrix groups, globally irreducible lattices, Mordell-Weil lattices, and more.

Articles in the volume represent expository lectures by leading experts on recent developments in the field. The book offers a comprehensive introduction to the current state of knowledge in the arithmetic theory of quadratic forms and provides active directions of research with new results. Topics addressed in the volume emphasize connections with related fields, such as group theory, arithmetic geometry, analytic number theory, and modular forms. The book is an excellent introductory guide for students as well as a rich reference source for researchers.

Readership

Graduate students and research mathematicians interested in number theory; computer scientists; information specialists.

Table of Contents

  • J. S. Hsia -- Arithmetic of indefinite quadratic forms
  • A. G. Earnest -- Universal and regular positive quadratic lattices over totally real number fields
  • W. K. Chan -- Class numbers of quaternary quadratic forms of discriminant 4\(p\)
  • A. Khosravani -- Universal quadratic and Hermitian forms
  • B. M. Kim, M.-H. Kim, and B.-K. Oh -- 2-universal positive definite integral quinary quadratic forms
  • Y. Kitaoka -- Finite arithmetic subgroups of \(GL_n\), VI
  • M. Jöchner -- On the representation theory of positive definite quadratic forms
  • T. Shioda -- Cyclotomic analogue in the theory of algebraic equations of type \(E_6, E_7, E_8\)
  • P. H. Tiep -- Globally irreducible lattices
  • B. H. Gross -- On simply-connected groups over \(\mathbf Z\), with \(G(\mathbf R)\) compact
  • P. Calame and M. Mischler -- \(F\)-lattices and genus of hermitian forms
  • D. G. James -- Primitive local densities for unimodular quadratic forms
  • Y. Hironaka -- Local densities of hermitian forms
  • D. R. Estes and K. Moon -- Form class groups over number fields
  • F. Xu -- Arithmetic Springer theorem on quadratic forms under field extensions of odd degree
  • A.-M. Bergé -- Classification of positive forms having prescribed automorphisms
  • G. Nebe -- Construction and investigation of lattices with matrix groups
  • R. Scharlau, A. Schiemann, and R. Schulze-Pillot -- Theta series of modular, extremal, and hermitian lattices
  • H. Katsurada -- Squared Möbius function for half-integral matrices
  • N. Dummigan -- Theta series congruences
  • M. Hisasue -- On a denominator of a certain formal power series attached to local densities
  • K.-i. Hashimoto -- Linear relations of theta series attached to Eichler orders of quaternion algebras
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