Publications:

• Equidistribution of $\alpha p^{\theta }$ with a Chebotarev condition and applications to extremal primes (with N. Prabhu), Mathematika, 68 (2022), no. 3, 595--619.
  


• Partitions into primes in arithmetic progressions, preprint.
  


• Hilbert transforms and the equidistribution of zeros of polynomials (with E. Carneiro, M. Das, A. Florea, A. Kumchev, M. Milinovich, C. T.-Butterbaugh, J. Wang), Journal of Functional Analysis 281 (2021), no. 9, Paper No. 109199, 25 pp.


• Extremal primes for elliptic curves without complex multiplication (with Chantal David, Ayla Gafni, Neha Prabhu, and Caroline T.-Butterbaugh), Proc. Amer. Math. Soc., 148 (2020), 929--943 [pdf]
  


• On the distribution of zeros of derivatives of the Riemann ξ-function (with Arindam Roy),
  Forum Math., (2020); 32(1): 1--22 [pdf]
  


• Four identities for third order mock theta functions (with George Andrews, Bruce Berndt, Song Heng Chan, and Sun Kim), Nagoya Math. J., 239 (2020), 173--204. DOI:10.1017/nmj.2018.35.


• Spatial statistics of Apollonian Gaskets (with Weiru Chen, Mo Jiao, Calvin Kessler, and Xin Zhang), Exp. Math. (2019), 28:3, 263-270, DOI: 10.1080/10586458.2017.1385037.


• Partitions into $k$th powers of terms in an arithmetic progression (with Bruce Berndt and Alexandru Zaharescu), Math. Z. (2018) 290:1277--1307 [pdf]
  


• Zeros of normalized combinations of ${\xi }^{\left(k\right)}\left(s\right)$ on Re$\left(s\right)=1/2$ (with Sneha Chaubey, Nicolas Robles, and Alexandru Zaharescu), J. Math. Anal. Appl., 461 (2018), no. 2, 1771--1785 [pdf]


• Divisibility properties of sporadic Apéry-like numbers (with Armin Straub), Research in Number Theory (2016), 2:5, 1--26 [pdf]


• Extensive parity analysis of broken $5$-diamond partitions (with Bernard L.S. Lin and Andrew Y.Z. Wang), Int. J. Number Theory 12 (2016), no. 1, 219--236 [pdf]


• Geometry of Farey-Ford Polygons (with Jayadev S. Athreya, Sneha Chaubey, and Alexandru Zaharescu), New York J. Math. 21 (2015), 637--656 [pdf]


• $k$-moments of distances between centers of Ford circles (with Sneha Chaubey and Alexandru Zaharescu), J. Math. Anal. Appl. 422 (2015), no. 2, 906--919 [pdf]


• On the parity of broken $k$-diamond partitions (with Sneha Chaubey, Wei Cheng and Alexandru Zaharescu), Ann. Univ. Ferrara Sez. VII Sci. Mat. 60 (2014), no. 2, 347--361 [pdf]


• The Siegel norm, the length function and character values of finite groups (with Florin Stan and Alexandru Zaharescu), Indag. Math. (N.S.) 25 (2014), no. 3, 475--486 [pdf]

Research awards/fellowships:

• AMS-Simons Travel Grant, 2017-19.


• Research Award, Rutgers University, 2018.


• Bateman Prize in Number Theory, UIUC, 2016-17.


• David G. Bourgin Mathematics Fellowship, UIUC, 2016-17.


• Bateman Fellowship in Number Theory, UIUC, 2015-16.


• Arnold O. Beckman Research Award (with B. C. Berndt), UIUC, 2014-15.