Timeline for Asymptotic estimate of the number of points of variety over finite field
Current License: CC BY-SA 4.0
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| Sep 20, 2020 at 13:54 | comment | added | Will Sawin | @makt For $X$ of dimension $1$, one can prove the weaker estimate by analytic number theory methods a la the usual proof of the prime number theorem over the integers (see Proposition 5.13 of Rosen's Number Theory in Function Fields). Maybe there is an analogue of the Erdős-Selberg elementary proof using Selberg's symmetry formula as well. | |
| Sep 20, 2020 at 13:21 | comment | added | asv | Many thanks. Fixed the missing condition. The Lang-Weil estimate seems to be much stronger than what I asked. Also the Riemann hypothesis for curves is not very elementary for my taste. In fact I do not have an elementary answer to my question even for the case of a curve. Is Riemann hypothesis necessary in the latter case? | |
| Sep 20, 2020 at 13:12 | history | answered | Will Sawin | CC BY-SA 4.0 |