My research interests: My research is currently supported by NSF grant DMS 1600494. Previous support: NSF grants DMS 1160720, DMS 1015173, DMS 0801191, DMS 0854900.

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1. Integrality of a ratio of Petersson norms and level-lowering congruences , Ann. of Math., (2), 163 (2006), no. 3, pp. 901-967.
   
   
2. Arithmetic properties of the theta correspondence and periods of modular forms , Eisenstein series and Applications, Progress in Math. 258, Birkhauser, 2008, pp. 251-269.
   
   
3. Arithmetic properties of the Shimura-Shintani-Waldspurger correspondence (with an appendix by Brian Conrad) , Invent. Math. 176, p. pp. 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, pp. 400-414.
   
   
5. On the Fourier coefficients of modular forms of half-integral weight , Forum Math. 22 (2010), no. 1, pp. 153-177.
   
   
6. Chow-Heegner points on CM elliptic curves and values of p-adic L-functions (with M. Bertolini and H. Darmon), IMRN, appeared online doi:10.1093/imrn/rns237, print version:Vol. 2014 (2014) pp. 745-793.
   
   
7. p-adic Rankin L-series and rational points on CM elliptic curves (with M. Bertolini and H. Darmon), Pacific Journal of Mathematics (Jonathan Rogawski Memorial Issue), Vol. 260, No. 2, 2012, pp. 261-303.
   
   
8. Generalized Heegner cycles and p-adic Rankin L-series (with M. Bertolini and H. Darmon; and an appendix by Brian Conrad), Duke Math Journal, Vol. 162, No. 6, 2013, pp. 1033-1148.
   
   
9. p-adic L-functions and the coniveau filtration on Chow groups (with M. Bertolini and H. Darmon; and an appendix by Brian Conrad), Crelle, to appear.
   
   
10. p-adic L-functions and Euler systems (Survey article, with M. Bertolini, F. Castella, H. Darmon, S. Dasgupta, V. Rotger), to appear in the Proceedings of the 2011 LMS-EPSRC Durham Symposium on Automorphic forms and Galois representations.
    
    
11. Periods of quaternionic Shimura varieties. I. (with A. Ichino), Preprint.
    
    
12. Automorphic cohomology, motivic cohomology and the adjoint L-function. (with A. Venkatesh), Preprint.
    
    
13. Hodge classes and the Jacquet-Langlands correspondence. (with A. Ichino), Preprint.