---
title: "Bibliography"
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part: "Lattices and Quadratic Forms"
chapter: "Lattices over Number Fields"
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---

# Bibliography

<a id="cite-belispinor"></a>
- **[Bel03]** C. N. Beli. Integral spinor norm groups over dyadic local fields. *J. Number Theory*, 102(1):125–182, 2003. URL: [http://dx.doi.org/10.1016/S0022-314X(03)00057-X](http://dx.doi.org/10.1016/S0022-314X(03)00057-X), [doi:10.1016/S0022-314X(03)00057-X](https://doi.org/10.1016/S0022-314X(03)00057-X).
<a id="cite-mr3347991"></a>
- **[Cho15]** S. Cho. Group schemes and local densities of quadratic lattices in residue characteristic 2. *Compos. Math.*, 151(5):793–827, 2015. URL: [http://dx.doi.org/10.1112/S0010437X14007829](http://dx.doi.org/10.1112/S0010437X14007829), [doi:10.1112/S0010437X14007829](https://doi.org/10.1112/S0010437X14007829).
<a id="cite-costellohsia"></a>
- **[CH87]** P. J. Costello and J. S. Hsia. Even Unimodular 12-Dimensional Quadratic Forms over ${\bf Q}(\sqrt 5)$. *Adv. Math.*, 64:241–278, 1987.
<a id="cite-mr1801770"></a>
- **[GY00]** W. T. Gan and J.-K. Yu. Group schemes and local densities. *Duke Math. J.*, 105(3):497–524, 2000. URL: [http://dx.doi.org/10.1215/S0012-7094-00-10535-2](http://dx.doi.org/10.1215/S0012-7094-00-10535-2), [doi:10.1215/S0012-7094-00-10535-2](https://doi.org/10.1215/S0012-7094-00-10535-2).
<a id="cite-mr1815252"></a>
- **[GHY01]** Wee Teck Gan, Jonathan P. Hanke, and Jiu-Kang Yu. On an exact mass formula of Shimura. *Duke Math. J.*, 107(1):103–133, 2001. URL: [http://dx.doi.org/10.1215/S0012-7094-01-10716-3](http://dx.doi.org/10.1215/S0012-7094-01-10716-3), [doi:10.1215/S0012-7094-01-10716-3](https://doi.org/10.1215/S0012-7094-01-10716-3).
<a id="cite-jac62"></a>
- **[Jac62a]** Ronald Jacobowitz. Hermitian forms over local fields. *Amer. J. Math.*, 84:441–465, 1962. URL: [https://doi.org/10.2307/2372982](https://doi.org/10.2307/2372982), [doi:10.2307/2372982](https://doi.org/10.2307/2372982).
<a id="cite-kirschmerhabil"></a>
- **[Kir16]** M. Kirschmer. *Definite quadratic and hermitian form with small class number*. Habilitation, RWTH Aachen University, 2016.
<a id="cite-kneser"></a>
- **[Kne57]** M. Kneser. Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen. *Archiv Math.*, 8:241–250, 1957.
<a id="cite-lorchphd"></a>
- **[Lor16]** D. Lorch. *Einklassige Geschlechter orthogonaler Gruppen*. PhD thesis, RWTH Aachen University, 2016.
<a id="cite-maass-4dim-lattice"></a>
- **[Maa41]** H. Maass. Modulformen und quadratische Formen über dem quadratischen Zahlkörper $R(\sqrt 5)$. *Math. Ann.*, 118:65–84, 1941.
<a id="cite-omeara"></a>
- **[OMe73]** O. T. O'Meara. *Introduction to Quadratic Forms*. Springer, 1973.
<a id="cite-mr1681092"></a>
- **[Shi99]** G. Shimura. An exact mass formula for orthogonal groups. *Duke Math. J.*, 97(1):1–66, 1999. URL: [http://dx.doi.org/10.1215/S0012-7094-99-09701-6](http://dx.doi.org/10.1215/S0012-7094-99-09701-6), [doi:10.1215/S0012-7094-99-09701-6](https://doi.org/10.1215/S0012-7094-99-09701-6).
<a id="cite-mr1503238"></a>
- **[Sie35]** C. L. Siegel. Über die analytische Theorie der quadratischen Formen. *Ann. of Math. (2)*, 36(3):527–606, 1935. URL: [http://dx.doi.org/10.2307/1968644](http://dx.doi.org/10.2307/1968644), [doi:10.2307/1968644](https://doi.org/10.2307/1968644).