Fernando Xuancheng Shao

Graduate student
Stanford University
Department of Mathematics
381-N Sloan Hall
Stanford, CA 94305

Email address: xshao at math dot stanford dot edu

I am a fifth year math PhD student at Stanford University. My advisor is Prof. K. Soundararajan. My research interests include analytic number theory and additive combinatorics.


In Spring 2014, I am a teaching assistant for Math 21.


  • On an inverse ternary Goldbach problem.

  • Finding linear patterns of complexity one. Int. Math. Res. Notices. To appear.

  • Carries, group theory, and additive combinatorics (with Persi Diaconis and Kannan Soundararajan). Amer. Math. Monthly

  • Large values of the additive energy in R^d and Z^d, Math. Proc. Camb. Phil. Soc. (2014) 156: 327–341.

  • A new proof of Vinogradov's three primes theorem.

  • Character sums over unions of intervals. Forum Math. To appear.

  • A density version of the Vinogradov three primes theorem, Duke Math. J. 163 (2014), no. 3, 489–512.

  • On character sums and exponential sums over generalized arithmetic progressions, Bull. Lond. Math. Soc. 45 (2013), no. 3, 541–550.