Subject Area: Modular forms, Galois representations

A central area in number theory is the study of special values of L-functions of automorphic forms, which are analytic objects. Many of the problems in number theory can be studied in terms of the L-function of certain automorphic forms. One fruitful way of studying the special values of these L-functions is through the p-adic interpolation of these values, for a prime p. This is carried out through the Bloch-Kato Tamagawa Number Conjecture and the Main Conjecture of Iwasawa theory. These conjectures relate the p-adic interpolation of special values of L-function which are analytic objects with arithmetic objects known as Selmer groups.

In a vast generalization, by considering an infinite extension of a number field whose Galois group is a p-adic Lie group, many deep and beautiful conjectures were formulated relating objects of arithmetic nature, again typified by a Selmer group of Galois representations and p-adic nature of their corresponding L-functions.

We have carried out a study of an important invariant that tells us about the structure of these Selmer groups. We are also interested in studying the p-adic nature of representations of Galois groups which are fundamental in understanding the Selmer groups.

- Iwasawa invariants for the false-Tate extension and congruences between modular forms, J. Number Theory 129 (2009), no. 8, 1893–1911.
- Non existence of finite
Λ-submodules of dual Selmer groups over a cyclotomic
ℤ
_{p}-extension, J. Ramanujan Math. Soc. 24 (2009), no. 1, 75–85. - On μ-invariants of Selmer groups of some CM elliptic curves, Int. J. Number Theory, 09, 1199 (2013). DOI: 10.1142/S1793042113500206.
- On the μ-invariant of fine Selmer groups, J. Number Theory (to appear).