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
- Subconvexity for L-functions of non-spherical cusp forms on GL(3), with V. Blomer, on the arXiv, to appear in Acta Arithmetica.
- The arithmetic Kuznetsov formula on GL(3), I: The Whittaker case, on the arXiv, to appear in Revista Matemática Iberoamericana.
- 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, to appear in the American Journal of Mathematics.
- 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, in Algebra & Number Theory (arXiv).
- Plancherel distribution of Satake parameters of Maass cusp forms on GL3, with F. Zhou, in International Mathematics Research Notices (arXiv).
- On the fourth moment of Hecke Maass forms and the Random Wave Conjecture, with R. Khan, in Compositio Mathematica (arXiv).
- 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 to appear in Annales scientifiques de l’École normale supérieure.
- The spectral Kuznetsov formula on SL(3), in the Transactions of the American Mathematical Society (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 Commentarii Mathematici Helvetici.
- 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.