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Significance Almost 100 years ago, Artin defined an analog of the famous Riemann zeta function for curves (one-dimensional varieties) over a finite field. In 2005, L.W. defined two different series of “higher zeta functions” for curves over finite fields that both generalized Artin’s zeta functions, one being defined geometrically and the other using advanced concepts from group representation theory, and conjectured that they always coincide. In this paper this conjecture is proved by giving a formula for one of the two series and showing that it agrees with the formula for the other series proved a few years ago by Sergey Mozgovoy and Markus Reineke.

Higher-rank zeta functions and SL n -zeta functions for curves

Higher-rank zeta functions and SL _n -zeta functions for curves