Publications and preprints

• Quartic Gauss sums over primes and metaplectic theta functions (with C. David, A. Hamieh, and H.Lin), Submitted [arxiv] 35pp.
• Bias in cubic Gauss sums: Patterson's conjecture (with M.Radziwill), Submitted [arxiv] 77 pp.   Quanta article      IFLScience article    Caltech article   Illinois news
• On a problem of Hoffstein and Kontorovich, Submitted [arxiv]   24pp.
• Bilinear forms in Weyl sums for modular square roots and applications (with B.Kerr, I.E. Shparlinksi and A. Zaharescu)  Adv. Math. 375 (2020).   [arxiv]  
• The twisted second moment of modular half integral weight L-functions (with A.Zaharescu), Submitted  [arxiv]  58pp.
• Maass forms and the mock theta function f(q)  (with S.Ahlgren)    
  Math Ann. 374 (2019), no. 3-4, 1681–1718. [arxiv]
• Sums of Kloosterman sums over primes in an arithmetic progression  (with A.Zaharescu)    ​

               Q.J. Math. 70 (2019), no. 1, 319-342.  [arxiv]

• Uniform estimates for sums of Kloosterman sums of half integral weight

​​               Res. Number Theory 4 (2018), no. 4, Art. 45, 21 pp. [arxiv]

• Polynomial partition asymptotics (with N.Robles)         

               J. Math. Anal. Appl. 459 (2018), no. 1 , 359-384. [arxiv] 

MPhil thesis

• Nahm's conjecture in the Cartan case, School of Mathematics and Physics, University of Queensland. [thesis]​