Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL, 61801
xiannan (at) illinois (dot) edu
I am a J.L. Doob Research Assistant Professor at the University of Illinois at Urbana-Champaign. Previously, I was a graduate student working with Professor Soundararajan.
I am interested in analytic number theory, specifically L-functions and objects related to them.
Papers and preprints
(with M. Radziwill) The Riemann-zeta function on vertical arithmetic progressions Preprint.
Additive twists of Fourier coefficients of GL(3) Maass forms. Preprint. To appear, Proceedings of the AMS.
(with Y. Lamzouri and K. Soundararajan) On the least quadratic non-residue, values of $L$-functions at $s=1$ and related problems.
(With V. Chandee) Lower bounds for small fractional moments of Dirichlet L-functions. Preprint. To appear, International Math Research Notices.
The smallest prime that does not split completely in a number field. To appear, Algebra and Number Theory. Preprint.
Upper bounds on L-functions at the edge of the critical strip. Link. International Math Research Notices. It is also available on arXiv. Pdf.
Variation of the Riemann $\Xi$ function off the critical line Link, Acta Arithmetica 137 (2009), 277-284. It is also available on arXiv.
In Fall of 2012, I am teaching Math 347 and Math 213. In Spring of 2012, I taught Math 453. In Fall of 2011, I taught Math 347.
Previously, at Stanford, I have taught Math 41, and Math 52, Math 52H, Math 53, and Math 19.