# Jonathan Hanke's Website

Research and Software in Number Theory

## Math Papers

Mathematics Papers/Preprints:

1. Probabilistic and Stochastic perspectives on instantaneously rebalanced constant-weighted portfolio strategies in an antisymmetric two stock market
(30 pages; preprint)
2. On \$K_4\$ of the Gaussian and Eisenstein Integers
(with H. Gangl, P.E. Gunnells, A. Schurmann, M.D. Sikiric, and D. Yasaki)
(10 pages; preprint on arxiv.org)
3. On the cohomology of linear groups over imaginary quadratic fields
(with H. Gangl, P.E. Gunnells, A. Schurmann, M.D. Sikiric, and D. Yasaki)
(22 pages; preprint on arxiv.org)
4. Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields (“Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms”, 111–130, AMS Contemporary Mathematics, vol 587, 2013)
(23 pages; preprint on arxiv.org) [Book, Google Books excerpt]
5. Enumerating maximal definite quadratic forms of bounded class number over Z in n \$\geq\$ 3 variables (20 pages; preprint on arxiv.org)
6. Explicit formulas for Masses of Ternary Quadratic Lattices of varying determinant over Number Fields (27 pages; preprint on arxiv.org)
7. The Structure of Masses of rank n Quadratic Lattices of varying determinant over Number Fields (38 pages; preprint on arxiv.org)
8. Notes on “Quadratic Forms and Automorphic Forms” (revised from the 2009 Arizona Winter School)
(“Quadratic and Higher Degree Forms”, Devel. in Math., Vol. 31, (2013) 109-168) ….. [Arxiv : Review, Article]
9. A proof of the S-genus Identities for Ternary Quadratic Forms (with A. Berkovich and W.C. Jagy)
(The Ramanujan Journal, Dec. 2012, Vol. 29, Issue 1-3, pp431–445) ….. [Arxiv : Review, Article]
10. Universal Quadratic Forms and the 290-Theorem (with M. Bhargava)
(preprint) [290-Theorem Website]
(Number theory, 147–164, CRM Proc. Lecture Notes, vol 36, 2004)
[PS, DVI, PDF: Review, Book, Google Books excerpt]
12. On a Local-Global Principle for Integral Quadratic Forms
(unpublished preprint) ….. [PS, DVI, PDF] ….. (website in progress)
13. Local Densities and Explicit Bounds for Representability by a Quadratic Form
(Duke Math. J. 124 (2004), no. 2, 351–388) ….. [PS, DVI, PDF : Review, Article, Software]
14. On an Exact Mass Formula of Shimura (with W. T. Gan and J. Yu)
(Duke Math. J. 107 (2001), no. 1, 103–133) ….. [PS, DVI, PDF : Review, Article]
15. An Exact Mass Formula for Quadratic Forms over Number Fields
(J. Reine Angew. Math. 584 (2005), 1–27) ….. [PS, DVI, PDF : Review, Journal]

### Mathematics Theses:

• An Exact Mass Formula for Quadratic Forms over Number Fields
(Ph.D. Thesis, Princeton University, under Prof. Goro Shimura) ….. [PS, DVI, PDF]
• Torsion on certain Elliptic Curves over Quadratic Fields
(Undergraduate Thesis, SUNY at StonyBrook, under Prof. Anthony Knapp) ….. [PS, DVI, PDF]

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Written by jonhanke

September 12th, 2011 at 6:22 am

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