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Mathematics of Computation

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Computing annihilators of class groups from derivatives of $ L$-functions


Authors: Jonathan W. Sands and Brett A. Tangedal
Journal: Math. Comp. 87 (2018), 2937-2953
MSC (2010): Primary 11R29, 11R42, 11Y40
DOI: https://doi.org/10.1090/mcom/3297
Published electronically: January 29, 2018
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Abstract: We computationally verify that certain group ring elements obtained from the first derivatives of abelian $ L$-functions at the origin annihilate ideal class groups. In our test cases, these ideal class groups are connected with cyclic extensions of degree 6 over real quadratic fields.


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Additional Information

Jonathan W. Sands
Affiliation: Department of Mathematics and Statistics, University of Vermont, 16 Colchester Ave. Burlington, Vermont 05401
Email: Jonathan.Sands@uvm.edu

Brett A. Tangedal
Affiliation: Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, North Carolina 27412
Email: batanged@uncg.edu

DOI: https://doi.org/10.1090/mcom/3297
Keywords: Stark's conjecture, abelian $L$-function
Received by editor(s): June 26, 2016
Received by editor(s) in revised form: May 17, 2017
Published electronically: January 29, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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