Browsing Faculty of Arts and Sciences by Keyword "number theory"

Now showing items 1-4 of 4

    • The ABC's of Number Theory 

      Elkies, Noam (Harvard University, 2007)
      The ABC conjecture is a central open problem in modern number theory, connecting results, techniques and questions ranging from elementary number theory and algebra to the arithmetic of elliptic curves to algebraic geometry ...

    • Absolute Hodge Cycles in Prismatic Cohomology 

      Nie, Tian (2021-09-09)
      In this thesis we construct the notion of absolute Hodge cycles in prismatic cohomology for abelian schemes. We show that they are compatible with their de Rham and p-adic components under comparison isomorphisms.

    • Lattices and codes with long shadows 

      Elkies, Noam (International Press, 1995)
      In an earlier paper we showed that any integral unimodular lattice L of rank n which is not isometric with Z^n has a characteristic vector of norm at most n-8. [A "characteristic vector" of L is a vector w in L such that ...

    • Shimura Curves for Level-3 Subgroups of the (2,3,7) Triangle Group and Some Other Examples 

      Elkies, Noam (Springer Verlag, 2006)
      The (2,3,7) triangle group is known to be associated with a quaternion algebra A/K ramified at two of the three real places of K=Q(cos2π/7) and unramified at all other places of K. This triangle group and its congruence ...