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Research Interests

      My research interests are in Number Theory and Representation Theory,
      with a special focus on Automorphic Forms and Special values of L-functions.

    The projects 1 and 2 listed below are supported by AMS-SIMONS Research Enhancement Grant for PUI Faculty (2023--2026).

Publications

  1. Moments of Rankin-Selberg L-functions of large weights.   (With A. Hamieh)
         In Progress

  2. Subconvexity bound for Rankin-Selberg L-functions: t-aspect.   (With K. Aggarwal)
         In Progress

  3. Large sums of Fourier coefficients of cusp forms.   (With C. Frechette, M. Gerbelli-Gauthier, and A. Hamieh)
        Submitted for Publication

  4. Additive twists of Fourier coefficients.  (With A. Hamieh and J. Streipel)
         In Progress

  5. An alternative approach to computing β(2k+1).   (With N. Wattanawanichkul)
         To appear in Integers (2023)

  6. Nonvanishing of central critical values of Rankin-Selberg convolutions for Hilbert modular forms.  (With A. Hamieh)
         Math. Z. 297 (2021), no.1-2, 81-97. [pdf]

  7. Equidistribution of signs for Hilbert modular forms of half-integral weight.   (With S. Kaushik and N. Kumar)
         Res. Number Theory, 4 (2018) no.2, Art 13, 10pp. [pdf]

  8. Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: the weight aspect.  (With A. Hamieh)
         Ramanujan J. 45 (2018) no.3, 615-637. [pdf]

  9. Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: the level aspect.  (With A. Hamieh)
         Trans. Amer. Math. Soc. 369 (2017) no.12, 8781-8797. [pdf]

  10. On the Nature of e^γ and Non-Vanishing of Derivatives of L-series at s=1/2.   (With M. R. Murty)
         J. Number Theory, 161 (2016) 444-456. [pdf]

  11. Sign changes of Fourier coefficients of Hilbert modular forms. (With J. Meher)
         J. Number Theory, 145 (2014) 230-244. [pdf]

  12. Non-Vanishing of Derivatives of L-functions attached to Hilbert Modular Forms.
         Int. J. Number Theory, 8 (2012) no.4, 1099-1105. [pdf]

  13. Notes on the arithmetic of Hilbert modular forms.   (With A. Raghuram)
         J. Ramanujan Math. Soc. 26 (2011) no.3, 261-319. [pdf]

Expository Paper (Non-Peer-Reviewed)

  1. Some Notes on Fourier Coefficients of Hilbert Modular Forms.
         Proceedings for Seventh Women in Number Theory in Japan (2014) 72-77.

Expository Notes



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