Transactions of the American Mathematical Society

Author(s): Alexandru Buium
Journal: Trans. Amer. Math. Soc. 357 (2005), 901-964.
MSC (2000): Primary 11G05, 11G30
Posted: October 19, 2004
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Abstract: If $L(a,s):=\sum_n c(n,a)n^{-s}$ is a family of ``geometric''

functions depending on a parameter

, then the function $(p,a)\mapsto c(p,a)$ , where

runs through the set of prime integers, is not a rational function and hence is not a function belonging to algebraic geometry. The aim of the paper is to show that if one enlarges algebraic geometry by ``adjoining a Fermat quotient operation'', then the functions

become functions in the enlarged geometry at least for

functions of curves and Abelian varieties.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 11G05, 11G30

Alexandru Buium
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
Email: buium@math.unm.edu

DOI: 10.1090/S0002-9947-04-03715-8
PII: S 0002-9947(04)03715-8
Received by editor(s): August 16, 2000
Received by editor(s) in revised form: May 14, 2002
Posted: October 19, 2004
Additional Notes: The author was partially supported by NSF grants DMS 9996078 and 0096946.
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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