The maximum number of points on a curve of genus 4 over F_8 is 25

Details The maximum number of points on a curve of genus 4 over F_8 is 25 The maximum number of points on a curve of genus 4 over F_8 is 25

2002-01-23

arxiv.org/abs/math/0201226v2

Mathematics

Number Theory

16 pages, 5 page appendix; replaced July 7, 2002. Paper by David Savitt with an Appendix by Kristin Lauter. Includes a collect

Scientific paper

This paper proves that the maximum number of rational points on a smooth,
absolutely irreducible genus 4 curve over the field of 8 elements is 25. The
body of the paper shows that 27 points is not possible using techniques from
algebraic geometry. The appendix shows that 26 points is not possible by
examining the zeta functions.

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