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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Explicit arithmetic intersection theory and computation of Néron-Tate heights
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by Raymond van Bommel, David Holmes and J. Steffen Müller HTML | PDF
Math. Comp. 89 (2020), 395-410 Request permission

Abstract:

We describe a general algorithm for computing intersection pairings on arithmetic surfaces. We have implemented our algorithm for curves over $\mathbb {Q}$, and we show how to use it to compute regulators for a number of Jacobians of smooth plane quartics, and to numerically verify the conjecture of Birch and Swinnerton-Dyer for the Jacobian of the split Cartan curve of level 13, up to squares.
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Additional Information
  • Raymond van Bommel
  • Affiliation: Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, Netherlands
  • MR Author ID: 1271408
  • Email: raymondvanbommel@gmail.com
  • David Holmes
  • Affiliation: Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, Netherlands
  • MR Author ID: 972881
  • ORCID: 0000-0002-6081-2516
  • Email: d.s.t.holmes@math.leidenuniv.nl
  • J. Steffen Müller
  • Affiliation: Bernoulli Institute, University of Groningen, Nijenborgh 9, 9747 AG Groningen, Netherlands
  • Email: steffen.muller@rug.nl
  • Received by editor(s): September 27, 2018
  • Received by editor(s) in revised form: February 11, 2019, and February 27, 2019
  • Published electronically: May 17, 2019
  • © Copyright 2019 American Mathematical Society
  • Journal: Math. Comp. 89 (2020), 395-410
  • MSC (2010): Primary 14G40; Secondary 11G30, 11G50, 37P30
  • DOI: https://doi.org/10.1090/mcom/3441
  • MathSciNet review: 4011549