**Contemporary Mathematics**

Volume: 249;
1999;
302 pp;
Softcover

MSC: Primary 11;
Secondary 20

Print ISBN: 978-0-8218-1949-4

Product Code: CONM/249

List Price: $110.00

Individual Member Price: $88.00

**Electronic ISBN: 978-0-8218-7839-2
Product Code: CONM/249.E**

List Price: $110.00

Individual Member Price: $88.00

# Integral Quadratic Forms and Lattices

Share this page *Edited by *
*Myung-Hwan Kim; John S. Hsia; Yoshiyuki Kitaoka; Rainer Schulze-Pillot*

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.

#### Table of Contents

# Table of Contents

## Integral Quadratic Forms and Lattices

- Contents vii8 free
- Preface ix10 free
- Arithmetic of indefinite quadratic forms 112 free
- Universal and regular positive quadratic lattices over totally real number fields 1728
- Class numbers of quaternary quadratic forms of discriminant 4p 2940
- Universal quadratic and hermitian forms 4354
- 2-universal positive definite integral quinary quadratic forms 5162
- Finite arithmetic subgroups of GLn, VI 6374
- On the representation theory of positive definite quadratic forms 7384
- Cyclotomic analogue in the theory of algebraic equations of type E6, E7, E8 8798
- Globally irreducible lattices 97108
- On simply-connected groups over Z, with G(R) compact 113124
- F-lattices and genus of hermitian forms 119130
- Primitive local densities for unimodular quadratic forms 129140
- Local densities of hermitian forms 135146
- Form class groups over number fields 149160
- Arithmetic Springer theorem on quadratic forms under field extensions of odd degree 175186
- Classification of positive forms having prescribed automorphisms 199210
- Construction and investigation of lattices with matrix groups 205216
- Theta series of modular, extremal, and hermitian lattices 221232
- Squared Möbius function for half-integral matrices 235246
- Theta series congruences 249260
- On a denominator of a certain formal power series attached to local densities 253264
- Linear relations of theta series attached to Eichler orders of quaternion algebras 261272

#### Readership

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