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Higher-rank zeta functions for elliptic curves

Lin Weng1, Don Zagier2,3

  • 1Graduate School of Mathematics, Kyushu University, 819-0395 Fukuoka, Japan; dbz@mpim-bonn.mpg.de weng@math.kyushu-u.ac.jp.

Proceedings of the National Academy of Sciences of the United States of America
|February 20, 2020
PubMed
Summary

This study proves the Riemann hypothesis for nonabelian zeta functions on genus 1 curves over finite fields. The research connects Dirichlet series of vector bundles to these zeta functions, confirming a key conjecture.

Keywords:
Riemann hypothesiselliptic curves over finite fieldshigher-rank zeta functionssemistable bundles

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