Contemporary Mathematics 1999; 302 pp; softcover Volume: 249 ISBN10: 0821819496 ISBN13: 9780821819494 List Price: US$110 Member Price: US$88 Order Code: CONM/249
 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, MordellWeil 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  2universal 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 simplyconnected 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. SchulzePillot  Theta series of modular, extremal, and hermitian lattices
 H. Katsurada  Squared Möbius function for halfintegral 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
