Max Wenqiang Xu, Real zeros of Fekete polynomials and positive definite characters (NTWS 217)

In 1911, Fekete proposed the problem of studying how likely a Fekete polynomial has no real zeros in [0,1]. The work of Baker and Montgomery in 1989 qualitatively showed that Fekete polynomials without real zeros in [0,1] are rare. A closely related question is asking how likely a quadratic character has nonnegative partial sums at any stopping point. In a joint work (in progress) with Angelo and Soundararajan, we give a quantitative upper bound which is close to the conjectural bound.
Link to slides: drive.google.com/file/d/1KuS2...
Number Theory Web Seminar: www.ntwebseminar.org
Original air date:
Thursday, June 20, 2024 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, June 21, 2024 (1am AEST, 3am NZST)