Department of Mathematics, Rutgers University

I am currently a Hill assistant professor at the Department of Mathematics, Rutgers University. I received my Ph.D. degree at the Ohio State University in May 2015. My thesis advisor is Roman Holowinsky.

My email address is "zhi.qi [at] rutgers [dot] edu".

My research concentrates on analytic number theory and representation theory, in particular, automorphic forms, L-functions and the theory of high-rank Bessel functions.

CV

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## Papers

"Subconvexity for Twisted $L$-Functions on $GL_3$ over $\mathbb{Q} (i)$." in preparation.

"Cancellation in the Additive Twists of Fourier Coefficients for $GL_2$ and $GL_3$ over Number Fields." to appear in Amer. J. Math., arXiv:1610.05380 (2016).

"On the Fourier Transform of Bessel Functions over Complex Numbers - II: the General Case." arXiv preprint arXiv:1607.01098 (2016).

"On the Fourier Transform of Bessel Functions over Complex Numbers - I: the Spherical Case." to appear in Monatsh. Math., arXiv:1606.02913 (2016).

"On the Kuznetsov Trace Formula for $\mathrm{PGL}_2(\mathbb{C})."J. Funct. Anal. 272, 3259–3280, 2017. "Theory of Fundamental Bessel Functions of High Rank." to appear in Mem. Amer. Math. Soc., arXiv:1612.03553 (2016). (This is a combination of the previous two Bessel papers as well as the first two chapters of my thesis.) "Theory of Bessel Functions of High Rank - II: Hankel Transforms and Fundamental Bessel Kernels." arXiv preprint arXiv:1411.6710 (2014). "Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions." arXiv preprint arXiv:1408.5652 (2014). joint with Roman Holowinsky and Ritabrata Munshi, "Character Sums of Composite Moduli and Hybrid Subconvexity." Advances in the Theory of Automorphic Forms and Their$L$-functions, 135-148, Contemp. Math., 664, Amer. Math. Soc., Providence, RI, 2016. joint with Roman Holowinsky and Ritabrata Munshi, "Hybrid Subconvexity Bounds for$L (1/2, \text{Sym}^2 f \otimes g)\$." Math. Z. 283, no. 1-2, 555–579, 2016.

"Morita's Duality for Split Reductive Groups." J. Number Theory, 132, 2012.

joint with Chang Yang, "Morita's Theory for the Symplectic Groups." Int. J. Number Theory, 07, 2011.

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## Thesis

"Theory of Bessel Functions of High Rank." Ph.D. Thesis, the Ohio State University, 2015.

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