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Book DetailsContemporary MathematicsVolume: 249; 1999; 302 ppMSC: Primary 11; Secondary 20;
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.ReadershipGraduate students and research mathematicians interested in number theory; computer scientists; information specialists.

Table of Contents

Articles

J. S. Hsia  Arithmetic of indefinite quadratic forms [ MR 1732345 ]

A. G. Earnest  Universal and regular positive quadratic lattices over totally real number fields [ MR 1732346 ]

Wai Kiu Chan  Class numbers of quaternary quadratic forms of discriminant $4p$ [ MR 1732347 ]

Azar Khosravani  Universal quadratic and Hermitian forms [ MR 1732348 ]

Byeong Moon Kim, MyungHwan Kim and ByeongKweon Oh  $2$universal positive definite integral quinary quadratic forms [ MR 1732349 ]

Yoshiyuki Kitaoka  Finite arithmetic subgroups of ${\rm GL}_n$. VI [ MR 1732350 ]

M. Jöchner  On the representation theory of positive definite quadratic forms [ MR 1732351 ]

Tetsuji Shioda  Cyclotomic analogue in the theory of algebraic equations of type $E_6,E_7,E_8$ [ MR 1732352 ]

Pham Huu Tiep  Globally irreducible lattices [ MR 1732353 ]

Benedict H. Gross  On simplyconnected groups over ${\bf Z}$, with $G({\bf R})$ compact [ MR 1732354 ]

Philippe Calame and Maurice Mischler  $F$lattices and genus of Hermitian forms [ MR 1732355 ]

Donald G. James  Primitive local densities for unimodular quadratic forms [ MR 1732356 ]

Yumiko Hironaka  Local densities of Hermitian forms [ MR 1732357 ]

Dennis R. Estes and Kyunghee Moon  Form class groups over number fields [ MR 1732358 ]

Fei Xu  Arithmetic Springer theorem on quadratic forms under field extensions of odd degree [ MR 1732359 ]

AnneMarie Bergé  Classification of positive forms having prescribed automorphisms [ MR 1732360 ]

Gabriele Nebe  Construction and investigation of lattices with matrix groups [ MR 1732361 ]

Rudolf Scharlau, Alexander Schiemann and Rainer SchulzePillot  Theta series of modular, extremal, and Hermitian lattices [ MR 1732362 ]

Hidenori Katsurada  Squared Möbius function for halfintegral matrices [ MR 1732363 ]

Neil Dummigan  Theta series congruences [ MR 1732364 ]

Masaki Hisasue  On a denominator of a certain formal power series attached to local densities [ MR 1732365 ]

Kiichiro Hashimoto  Linear relations of theta series attached to Eichler orders of quaternion algebras [ MR 1732366 ]


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

Articles

J. S. Hsia  Arithmetic of indefinite quadratic forms [ MR 1732345 ]

A. G. Earnest  Universal and regular positive quadratic lattices over totally real number fields [ MR 1732346 ]

Wai Kiu Chan  Class numbers of quaternary quadratic forms of discriminant $4p$ [ MR 1732347 ]

Azar Khosravani  Universal quadratic and Hermitian forms [ MR 1732348 ]

Byeong Moon Kim, MyungHwan Kim and ByeongKweon Oh  $2$universal positive definite integral quinary quadratic forms [ MR 1732349 ]

Yoshiyuki Kitaoka  Finite arithmetic subgroups of ${\rm GL}_n$. VI [ MR 1732350 ]

M. Jöchner  On the representation theory of positive definite quadratic forms [ MR 1732351 ]

Tetsuji Shioda  Cyclotomic analogue in the theory of algebraic equations of type $E_6,E_7,E_8$ [ MR 1732352 ]

Pham Huu Tiep  Globally irreducible lattices [ MR 1732353 ]

Benedict H. Gross  On simplyconnected groups over ${\bf Z}$, with $G({\bf R})$ compact [ MR 1732354 ]

Philippe Calame and Maurice Mischler  $F$lattices and genus of Hermitian forms [ MR 1732355 ]

Donald G. James  Primitive local densities for unimodular quadratic forms [ MR 1732356 ]

Yumiko Hironaka  Local densities of Hermitian forms [ MR 1732357 ]

Dennis R. Estes and Kyunghee Moon  Form class groups over number fields [ MR 1732358 ]

Fei Xu  Arithmetic Springer theorem on quadratic forms under field extensions of odd degree [ MR 1732359 ]

AnneMarie Bergé  Classification of positive forms having prescribed automorphisms [ MR 1732360 ]

Gabriele Nebe  Construction and investigation of lattices with matrix groups [ MR 1732361 ]

Rudolf Scharlau, Alexander Schiemann and Rainer SchulzePillot  Theta series of modular, extremal, and Hermitian lattices [ MR 1732362 ]

Hidenori Katsurada  Squared Möbius function for halfintegral matrices [ MR 1732363 ]

Neil Dummigan  Theta series congruences [ MR 1732364 ]

Masaki Hisasue  On a denominator of a certain formal power series attached to local densities [ MR 1732365 ]

Kiichiro Hashimoto  Linear relations of theta series attached to Eichler orders of quaternion algebras [ MR 1732366 ]