Now showing items 1-11 of 11

    • 2-Selmer groups and Heegner points on elliptic curves 

      Li, Chao (2015-05-07)
      This thesis studies several aspects of the arithmetic of elliptic curves. In particular, we explore the prediction of the Birch and Swinnerton-Dyer conjecture when the 2-Selmer group has rank one. For certain elliptic ...
    • The Arithmetic of Simple Singularities 

      Thorne, Jack A. (2012-08-10)
      We investigate some arithmetic orbit problems in representations of linear algebraic groups arising from Vinberg theory. We aim to give a description of the orbits in these representations using methods with an emphasis ...
    • Automorphisms of Even Unimodular Lattices and Unramified Salem Numbers 

      Gross, Benedict H.; McMullen, Curtis T. (Elsevier, 2002)
      In this paper we study the characteristic polynomials \(S(x)=\det(xI−F| II_{p,q})\) of automorphisms of even unimodular lattices with signature \((p,q)\). In particular, we show that any Salem polynomial of degree \(2n\) ...
    • Cyclotomic Factors of Coxeter Polynomials 

      Gross, Benedict H.; Hironaka, Eriko; McMullen, Curtis T. (Elsevier, 2009)
      In this paper we show that the cyclotomic factors of the En Coxeter polynomials depend only on the value of \(n\) mod 360, and come exclusively from spherical subdiagrams.
    • A Formula for Some Shalika Germs 

      Tsai, Cheng-Chiang (2015-05-17)
      In this article, for nilpotent orbits in (the Lie algebras of) ramified quasi-split unitary groups with two Jordan blocks, we give the values of their Shalika germs at certain equi-valued elements with half-integral depth ...
    • On Cubic Rings and Quaternion Rings 

      Gross, Benedict H.; Lucianovic, Mark (Elsevier, 2009)
      In this paper, we show that the orbits of some simple group actions parametrize cubic rings and quaternion rings.
    • On Newforms for Split Special Odd Orthogonal Groups 

      Tsai, Pei-Yu (2013-09-18)
      The theory of local newforms has been studied for the group of \(PGL_n\) and recently \(PGSp_4\) and some other groups of small ranks. In this dissertation, we develop a newform theory for generic supercuspidal representations ...
    • On the Arithmetic of Hyperelliptic Curves 

      Bland, Jason Charles (2016-05-06)
      My research involves answering various number-theoretic questions involving hyperelliptic curves. A hyperelliptic curve is a generalization of elliptic curves to curves of higher genus but which still have explicit ...
    • On the Moy-Prasad Filtration and Stable Vectors 

      Fintzen, Jessica (2016-05-19)
      Let K be a maximal unramified extension of a nonarchimedean local field of residual characteristic p > 0. Let G be a reductive group over K which splits over a tamely ramified extension of K. To a point x in the Bruhat–Tits ...
    • Pencils of quadrics and Jacobians of hyperelliptic curves 

      Wang, Xiaoheng (2013-10-08)
      Using pencils of quadrics, we study a construction of torsors of Jacobians of hyperelliptic curves twice of which is Pic^1. We then use this construction to study the arithmetic invariant theory of the actions of SO2n+1 ...
    • A Rigid Irregular Connection on the Projective Line 

      Frenkel, Edward; Gross, Benedict H. (Princeton University, 2009)
      In this paper we construct a connection ∇ on the trivial G-bundle on P1 for any simple complex algebraic group G, which is regular outside of the points 0 and ∞, has a regular singularity at the point 0, with principal ...