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.
Arithmetic of indefinite quadratic forms by J. S. Hsia Universal and regular positive quadratic lattices over totally real number fields by A. G. Earnest Class numbers of quaternary quadratic forms of discriminant 4$p$ by W. K. Chan Universal quadratic and Hermitian forms by A. Khosravani 2-universal positive definite integral quinary quadratic forms by B. M. Kim, M.-H. Kim, and B.-K. Oh Finite arithmetic subgroups of $GL n$, VI by Y. Kitaoka On the representation theory of positive definite quadratic forms by M. Jochner Cyclotomic analogue in the theory of algebraic equations of type $E 6, E 7, E 8$ by T. Shioda Globally irreducible lattices by P. H. Tiep On simply-connected groups over $\mathbf Z$, with $G(\mathbf R)$ compact by B. H. Gross $F$-lattices and genus of hermitian forms by P. Calame and M. Mischler Primitive local densities for unimodular quadratic forms by D. G. James Local densities of hermitian forms by Y. Hironaka Form class groups over number fields by D. R. Estes and K. Moon Arithmetic Springer theorem on quadratic forms under field extensions of odd degree by F. Xu Classification of positive forms having prescribed automorphisms by A.-M. Berge Construction and investigation of lattices with matrix groups by G. Nebe Theta series of modular, extremal, and hermitian lattices by R. Scharlau, A. Schiemann, and R. Schulze-Pillot Squared Mobius function for half-integral matrices by H. Katsurada Theta series congruences by N. Dummigan On a denominator of a certain formal power series attached to local densities by M. Hisasue Linear relations of theta series attached to Eichler orders of quaternion algebras by K.-i. Hashimoto.
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