Spacing of zeros of Hecke L-functions and the class number problem
| dc.creator | Conrey, J. Brian | |
| dc.creator | Iwaniec, Henryk | |
| dc.date | 2001-11-01 | |
| dc.date.accessioned | 2026-07-07T04:44:12Z | |
| dc.date.available | 2026-07-07T04:44:12Z | |
| dc.description | We derive strong and effective lower bounds for the class number h(q) of the imaginary quadratic field Q(\sqrt{-q}), conditionally subject to the existence of many small (subnormal) gaps between zeros of the L-function associated with a character of the class group associated with this field. In particular, we prove that if the gap between consecutive zeros of the L-function is somewhat smaller than the average for sufficiently many pairs of zeros on the critical line, then h >> \sqrt q (log q)^{-A} for some constant A > 0. For the trivial character, the L-function is the Dedekind zeta-function of the number field and so contains the Riemann zeta-function as a factor. Thus, as a corollary to our main result, we prove that this lower bound for h follows from the hypothesis that there are sufficiently many pairs of adjacent zeros of the Riemann zeta-function on the critical line whose spacing is slightly smaller than 1/2 of the average spacing. | |
| dc.description | 61 pages | |
| dc.identifier | https://arxiv.org/abs/math/0111012 | |
| dc.identifier | http://arxiv.org/abs/math/0111012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62545 | |
| dc.subject | Number Theory | |
| dc.title | Spacing of zeros of Hecke L-functions and the class number problem | |
| dc.type | text |