# Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms

### About this Title

**Wai Kiu Chan**, *Wesleyan University, Middletown, CT*, **Lenny Fukshansky**, *Claremont McKenna College, Claremont, CA*, **Rainer Schulze-Pillot**, *Universität des Saarlandes, Saarbrucken, Germany* and **Jeffrey D. Vaaler**, *University of Texas at Austin, Austin, TX*, Editors

Publication: Contemporary Mathematics

Publication Year
2013: Volume 587

ISBNs: 978-0-8218-8318-1 (print); 978-0-8218-9503-0 (online)

DOI: http://dx.doi.org/10.1090/conm/587

### Table of Contents

**Front/Back Matter**

**Articles**

- Gabriele Nebe – Boris Venkov’s Theory of Lattices and Spherical Designs
- Juan M. Cerviño and Georg Hein – Generalized Theta Series and Spherical Designs
- Wai Kiu Chan and Byeong-Kweon Oh – Representations of integral quadratic polynomials
- Renaud Coulangeon and Gabriele Nebe – Dense lattices as Hermitian tensor products
- Rainer Dietmann – Small zeros of homogeneous cubic congruences
- A. G. Earnest and Ji Young Kim – Strictly Regular Diagonal Positive Definite Quaternary Integral Quadratic Forms
- Lenny Fukshansky – Heights and quadratic forms: Cassels’ theorem and its generalizations
- Juan José Alba González and Florian Luca – On the positive integers $n$ satisfying the equation $F_n = x^2 + n y^2$
- Jonathan Hanke – Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields
- D. R. Heath-Brown – $p$-adic Zeros of Systems of Quadratic Forms
- David Kettlestrings and Jeffrey Lin Thunder – The Number of Function Fields with Given Genus
- Gregory T. Minton – Unique Factorization in the Theory of Quadratic Forms
- Gabriele Nebe – Golden lattices
- Rudolf Scharlau – The extremal lattice of dimension 14, level 7 and its genus
- Achill Schürmann – Strict Periodic Extreme Lattices
- C. L. Stewart – Exceptional units and cyclic resultants, II
- Jeffrey D. Vaaler and Martin Widmer – A note on generators of number fields
- Takao Watanabe, Syouji Yano and Takuma Hayashi – Voronoï’s reduction theory of $GL_n$ over a totally real number field
- Mark Watkins – Some comments about Indefinite LLL