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Integral Quadratic Forms and Lattices
 
Edited by: Myung-Hwan Kim Seoul National University, Seoul, Korea
John S. Hsia Ohio State University, Columbus, OH
Yoshiyuki Kitaoka Nagoya University, Nagoya, Japan
Rainer Schulze-Pillot Universität des Saarlandes, Saabrücken, Germany
Integral Quadratic Forms and Lattices
Softcover ISBN:  978-0-8218-1949-4
Product Code:  CONM/249
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7839-2
Product Code:  CONM/249.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-1949-4
eBook: ISBN:  978-0-8218-7839-2
Product Code:  CONM/249.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Integral Quadratic Forms and Lattices
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Integral Quadratic Forms and Lattices
Edited by: Myung-Hwan Kim Seoul National University, Seoul, Korea
John S. Hsia Ohio State University, Columbus, OH
Yoshiyuki Kitaoka Nagoya University, Nagoya, Japan
Rainer Schulze-Pillot Universität des Saarlandes, Saabrücken, Germany
Softcover ISBN:  978-0-8218-1949-4
Product Code:  CONM/249
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7839-2
Product Code:  CONM/249.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-1949-4
eBook ISBN:  978-0-8218-7839-2
Product Code:  CONM/249.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 2491999; 302 pp
    MSC: 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, 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
     
     
    • 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, Myung-Hwan Kim and Byeong-Kweon 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 simply-connected 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 ]
    • Anne-Marie 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 Schulze-Pillot — Theta series of modular, extremal, and Hermitian lattices [ MR 1732362 ]
    • Hidenori Katsurada — Squared Möbius function for half-integral 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 ]
    • Ki-ichiro Hashimoto — Linear relations of theta series attached to Eichler orders of quaternion algebras [ MR 1732366 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2491999; 302 pp
MSC: 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, 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.

  • 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, Myung-Hwan Kim and Byeong-Kweon 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 simply-connected 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 ]
  • Anne-Marie 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 Schulze-Pillot — Theta series of modular, extremal, and Hermitian lattices [ MR 1732362 ]
  • Hidenori Katsurada — Squared Möbius function for half-integral 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 ]
  • Ki-ichiro Hashimoto — Linear relations of theta series attached to Eichler orders of quaternion algebras [ MR 1732366 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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