Abstract
L. Solomon recently introduced a wide-ranging but concrete generalization of the Riemann and Dedkind zeta functions, as well as of Hey's zeta function for a simple algebra over the rationals. The coefficients of Solomon's zeta function give the numbers of certain types of sublattices in a given lattice over an order in a semisimple rational algebra. This paper studies the analogous zeta function and coefficients which arise for an order in a semi-simpleF q (X) -algebra, whereF q (X) is a field of rational functions over a finite fieldF q . Use is made of the analogues for function fields of results on his zeta functions which were first conjectured by Solomon, and later established by C J Bushnell and l Reiner.
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References
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Knopfmacher, J. Solomon's zeta functions over algebraic function fields. Manuscripta Math 53, 101–106 (1985). https://doi.org/10.1007/BF01174013
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DOI: https://doi.org/10.1007/BF01174013