Nice equations for nice groups |
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Authors: | Shreeram S Abhyankar |
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Institution: | (1) All Souls College, OX1 4AL Oxford, England |
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Abstract: | There are various natural local zeta functions associated with groups and rings for each primep. We consider the question of how these functions behave as we vary the primep and the groups (or rings) range over a specific class of groups (or rings), e.g. finitely generated torsion-free nilpotent
groups of a fixed Hirsch length orp-adic analytic groups of a fixed dimension. Using a result of Macintyre’s on the uniformity of parameterizedp-adic integrals, together with various natural parameter spaces we define for these classes of groups, we prove a strong finiteness
theorem on the possible poles of these local zeta functions. |
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