My research interests: My main interests are in the study of special values of L-functions (and their derivatives) and related themes such as Shimura varieties, automorphic forms, periods, theta functions and Iwasawa theory. My research is currently supported by NSF grants DMS 1160720 and DMS 0854900. Previous support: NSF grants DMS 1015173, DMS 0801191

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1. Integrality of a ratio of Petersson norms and level-lowering congruences , Ann. of Math., (2), 163 (2006), no. 3, 901-967.
   
   
2. Arithmetic properties of the theta correspondence and periods of modular forms , Eisenstein series and Applications, Progress in Math. 258, Birkhauser, 2008, 251-269.
   
   
3. Arithmetic properties of the Shimura-Shintani-Waldspurger correspondence (with an appendix by Brian Conrad) , Invent. Math. 176, p. 521-600 (2009).
   
   
4. On p-adic properties of central values of quadratic twists of an elliptic curve , Canad. J. Math. 62 (2010), no. 2, 400-414.
   
   
5. On the Fourier coefficients of modular forms of half-integral weight , Forum Math. 22 (2010), no. 1, 153-177.
   
   
6. Generalised Heegner cycles and p-adic Rankin L-series (joint with M. Bertolini and H. Darmon; with an appendix by Brian Conrad), Duke Math Journal, to appear.
   
   
7. p-adic Rankin L-series and rational points on CM elliptic curves (joint with M. Bertolini and H. Darmon), submitted.
   
   
8. Chow-Heegner points on CM elliptic curves and values of p-adic L-functions (joint with M. Bertolini and H. Darmon), IMRN, to appear.