Papers by Jonathan Hanke!

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Financial Mathematics Papers

Probabilistic and Stochastic perspectives on instantaneously rebalanced constant-weighted portfolio strategies in an antisymmetric two stock market; 30 pages.

Number Theory Papers

On K4 of the Gaussian and Eisenstein integers
with H. Gangl, P.E. Gunnells, A. Schurmann, M.D. Sikirić and D. Yasaki; 10 pages.

On the cohomology of linear groups over imaginary quadratic fields
with H. Gangl, P.E. Gunnells, A. Schurmann, M.D. Sikirić and D. Yasaki; 22 pages.

Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields
“Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms”,
Contemporary Mathematics, Volume 587, 2013, pp111-130; 24 pages.

Enumerating maximal definite quadratic forms of bounded class number over Z in n≥3 variables
20 pages.

Explicit formulas for masses of ternary quadratic lattices of varying determinant over number fields
27 pages.

The structure of masses of rank n quadratic lattices of varying determinant over number fields
38 pages.

Notes on “Quadratic and Automorphic Forms”
2009 Arizona Winter School on “Quadratic Forms”;
“Quadratic and Higher Degree Forms”, Devel. in Math., Volume 31, 2013, pp109-168; 73 pages.

A proof of the S-genus identities for ternary quadratic forms
with Alexander Berkovich and William C. Jagy
The Ramanujan Journal, December 2012, Volume 29, Issue 1-3, pp431-445; 14 pages.

Universal quadratic forms and the 290-Theorem
with Manjul Bhargava; 16 pages.

On an exact mass formula of Shimura
with Wee Teck Gan and Jiu-Kang Yu; Duke Math. J. 107 (2001), no. 1, 103–133.

An exact mass formula for quadratic forms over number fields
J. Reine Angew. Math. 584 (2005), 1–27.

Local densities and explicit bounds for representability by a quadratic form
Duke Math. J. 124 (2004), no. 2, 351–388.

Some recent results about (ternary) quadratic forms
Number theory, 147–164, CRM Proc. Lecture Notes 36, 2004.

On a local-global principle for quadratic forms
Unpublished preprint, 2003.

An exact mass formula for quadratic forms over number fields
Ph.D. thesis under the supervision of Prof. Goro Shimura, Spring 1999.

Torsion on certain elliptic curves over quadratic fields
Undergraduate thesis under the supervision of Prof. Anthony Knapp, Spring 1995.