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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The Igusa local zeta functions of elliptic curves


Authors: Diane Meuser and Margaret Robinson
Journal: Math. Comp. 71 (2002), 815-823
MSC (2000): Primary 11S40, 11G07
Published electronically: September 17, 2001
MathSciNet review: 1885630
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Abstract: We determine the explicit form of the Igusa local zeta function associated to an elliptic curve. The denominator is known to be trivial. Here we determine the possible numerators and classify them according to the Kodaira-Néron classification of the special fibers of elliptic curves as determined by Tate's algorithm.


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Additional Information

Diane Meuser
Affiliation: Boston University, Boston, Massachusetts 02215
Email: dmm@math.bu.edu

Margaret Robinson
Affiliation: Mount Holyoke College, South Hadley, Massachusetts 01075
Email: robinson@mtholyoke.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01396-5
PII: S 0025-5718(01)01396-5
Keywords: Local zeta functions, elliptic curves
Received by editor(s): July 10, 2000
Published electronically: September 17, 2001
Additional Notes: This work was supported by National Science Foundation Grant No. DMS-9732228
Article copyright: © Copyright 2001 American Mathematical Society