My current research is on the use of techniques from classical analytic number theory in the study of higher-rank automorphic forms.
I hope to apply these methods to classical equidistribution problems and problems related to polynomials and primes.
My interests and methods are in analytic number theory, harmonic analysis on symmetric spaces, complex analysis, the spectral theory of autormorphic forms, trace formulas, exponential sums, and L-functions.
NSF Grant DMS-1601919
- The arithmetic Kuznetsov formula on GL(3), I: The Whittaker case, on the arXiv.
- Kuznetsov, Petersson and Weyl on GL(3), II: The generalized principal series forms, on the arXiv.
- Kuznetsov, Petersson and Weyl on GL(3), I: The principal series forms, on the arXiv.
- Weights, raising and lowering operators, and K-types for automorphic forms on SL(3,ℝ), with S. D. Miller, on the arXiv.
- Higher weight on GL(3), II: The cusp forms, on the arXiv.
- Plancherel distribution of Satake parameters of Maass cusp forms on GL3, with F. Zhou, on the arXiv.
- On the fourth moment of Hecke Maass forms and the Random Wave Conjecture, with R. Khan, on the arXiv, to appear in Compo. Math.
- Higher weight on GL(3), I: The Eisenstein series, in Forum Mathematicum (arXiv).
- Global decomposition of GL(3) Kloosterman sums and the spectral large sieve, with V. Blomer, in Crelle's Journal (arXiv).
- On the subconvexity problem for L-functions on GL(3), with V. Blomer, on the arXiv.
- The spectral Kuznetsov formula on SL(3), in the Transactions of the AMS (arXiv).
- A mean value of a triple product of L-functions, with R. Khan, in Mathematische Zeitschrift (arXiv).
- Applications of the Kuznetsov formula on GL(3), II: the level aspect, with V. Blomer and P. Maga, in the Mathematische Annalen (arXiv).
- L4 norms of Hecke newforms of large level, with R. Khan, in the Mathematische Annalen (arXiv).
- A Sato-Tate law for GL(3), with V. Blomer and N. Raulf, in Comm. Math. Helv.
- On Sums of SL(3,ℤ) Kloosterman Sums. In the Ramanujan Journal (arXiv).
- UCLA Doctoral Thesis -- On Sums of SL(3,ℤ) Kloosterman Sums.
- A note on the Waring-Goldbach problem. In the Journal of Number Theory.
- A translation of Hadamard's Sur la distribution des zéros de la function ζ(s) et ses conséquences arithmétiques.