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Algorithmic Number Theory Symposium

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Algorithmic Number Theory Symposium (ANTS) is a biennial academic conference, first held in Cornell in 1994, constituting an international forum for the presentation of new research in computational number theory. They are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, arithmetic geometry, finite fields, and cryptography.[1]

Selfridge Prize[edit]

In honour of the many contributions of John Selfridge to mathematics, the Number Theory Foundation has established a prize to be awarded to those individuals who have authored the best paper accepted for presentation at ANTS. The prize, called the Selfridge Prize, is awarded every two years in an even numbered year. The prize winner(s) receive a cash award and a sculpture.

The prize winners and their papers selected by the ANTS Program Committee are:

  • 2006 – ANTS VII – Werner Bley and Robert Boltje – Computation of locally free class groups.[2]
  • 2008 – ANTS VIII – Juliana Belding, Reinier Bröker, Andreas Enge and Kristin LauterComputing hilbert class polynomials.[3]
  • 2010 – ANTS IX – John Voight – Computing automorphic forms on Shimura curves over fields with arbitrary class number.[4]
  • 2012 – ANTS X – Andrew SutherlandOn the evaluation of modular polynomials.[5]
  • 2014 – ANTS XI – Tom Fisher – Minimal models for 6-coverings of elliptic curves.[6]
  • 2016 – ANTS XII – Jan Steffen Müller and Michael Stoll – Computing canonical heights on elliptic curves in quasi-linear time.[7]
  • 2018 – ANTS XIII – Michael Musty, Sam Schiavone, Jeroen Sijsling and John Voight – A database of Belyĭ maps.[8]
  • 2020 – ANTS XIV – Jonathan Love and Dan BonehSupersingular curves with small non-integer endomorphisms.[9]
  • 2022 – ANTS XV – Harald Helfgott and Lola Thompson – Summing mu(n): a faster elementary algorithm.[10]


Prior to ANTS X, the refereed Proceedings of ANTS were published in the Springer Lecture Notes in Computer Science (LNCS). The proceedings of ANTS X, ANTS XIII, and ANTS XIV were published in the Mathematical Sciences Publishers Open Book Series (OBS). The proceedings of ANTS XI and ANTS XII were published as a special issue of the LMS Journal of Computation and Mathematics (JCM). The proceedings for ANTS XV will be published in Research in Number Theory.[11]


*Moved online due to COVID-19.


  1. ^ "Algorithmic Number Theory Symposium". Retrieved 14 March 2020.
  2. ^ Warner Bley; Robert Boltie (2006). "Computation of Locally Free Class Groups". Algorithmic Number Theory. Lecture Notes in Computer Science. Vol. 4076. pp. 72–86. doi:10.1007/11792086_6. ISBN 978-3-540-36075-9.
  3. ^ Juliana Belding; Reinier Bröker; Andreas Enge; Kristin Lauter (2008). "Computing Hilbert Class Polynomials". Algorithmic Number Theory. Lecture Notes in Computer Science. Vol. 5011. pp. 282–295. arXiv:0802.0979. doi:10.1007/978-3-540-79456-1_19. ISBN 978-3-540-79455-4. S2CID 11047044.
  4. ^ John Voight (2010). "Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number". Algorithmic Number Theory. Lecture Notes in Computer Science. Vol. 6197. pp. 357–37'. arXiv:1004.5340. doi:10.1007/978-3-642-14518-6_28. ISBN 978-3-642-14517-9. S2CID 15424318.
  5. ^ Andrew Sutherland (2012). "On the evaluation of modular polynomials". The Open Book Series. 1: 531–555. arXiv:1202.3985. Bibcode:2012arXiv1202.3985S. doi:10.2140/obs.2013.1.531. S2CID 1367368.
  6. ^ Tom Fisher, Fisher, Tom (2014). "Minimal models of 6-coverings of elliptic curves". LMS Journal of Computation and Mathematics. 17: 112–127. doi:10.1112/S1461157014000217.
  7. ^ Jan Steffen Müller; Michael Stoll (2016). "Computing Canonical Heights on Elliptic Curves in Quasi-Linear Time". LMS Journal of Computation and Mathematics. 19: 391–405. arXiv:1509.08748. doi:10.1112/S1461157016000139. S2CID 50736998.
  8. ^ Michael Musty; Sam Schiavone; Jeroen Sijsling; John Voight (2019). "A database of Belyi maps". The Open Book Series. 2: 375–392. arXiv:1805.07751. doi:10.2140/obs.2019.2.375. S2CID 119152099.
  9. ^ Jonathan Love; Dan Boneh (2020). "Supersingular curves with small non-integer endomorphisms". The Open Book Series. 4: 7–22. arXiv:1910.03180. doi:10.2140/obs.2020.4.7. S2CID 203905885.
  10. ^ Harald Helfgott; Lola Thompson (2022). "Summing mu(n): a faster elementary algorithm" (PDF). arXiv:2101.08773. {{cite journal}}: Cite journal requires |journal= (help)
  11. ^ "Call for Papers". ANTS XV. University of Bristol. Retrieved 10 August 2022.

External links[edit]