Fredrik Prüzelius

Two thirds of the zeros of Dirichlet L-functions at polylogarithmic height are simple and on the critical line, on average

Preprint (Version 2.3-draft, 18 August 2026). We outline a proof that for every sufficiently large prime q, at least 2/3 − O(1/log log q) of the zeros of the Dirichlet L-functions L(s, χ) in windows (T, 2T] at polylogarithmic height, averaged over the q−2 non-principal characters...

Two thirds of the zeros of Dirichlet L-functions at polylogarithmic height are simple and on the critical line, on average

Preprint (Version 2.3.1-draft, 18 August 2026). We outline a proof that for every sufficiently large prime q, at least 2/3 − O(1/log log q) of the zeros of the Dirichlet L-functions L(s, χ) in windows (T, 2T] at polylogarithmic height, averaged over the q−2 non-principal characte...