Professor Weston studies the interplay between L-functions and certain arithmetic objects known as Selmer groups. Selmer groups are generalizations of ideal class groups and the group of rational points on an elliptic curve which distill the information contained in p-adic representations of the absolute Galois group. He has used such relations to enlarge dramatically the number of cases in which one can precisely compute universal deformation rings as in the work of Wiles. Jointly with Robert Pollack of Boston University, he also studies the behavior of L-functions and Selmer groups of modular forms in certain p-adic analytic families. In many cases they are able to show that one can use values of the L-functions (which are relatively computable) to compute Selmer groups (which are a priori very difficult to compute).
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Power Residues of Fourier Coefficients of Elliptic Curves with Complex Multiplication (with E Zaurova), International Journal of Number Theory (2009)
Fix m greater than one and let E be an elliptic curve over Q with...
Local torsion on elliptic curves and the deformation theory of galois representations (with C David), Mathematical Research Letters (2008)
We prove that, on average, elliptic curves over Q have finitely many primes p for...
On Anticyclotomic Ì-Invariants of Modular Forms (with R Pollack), Mathematics and Statistics Department Faculty Publication Series (2006)
Variation of Iwasawa invariants in Hida families (with M Emerton and R Pollack), Inventiones Mathematicae (2006)
Let r : G_Q -> GL_2(Fpbar) be a p-ordinary and p-distinguished irreducible residual modular Galois...