John Jones - Publications

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Papers

  1. Mixed degree number field computations, with D. Roberts, submitted.
  2. Artin L-functions of small conductor, with D. Roberts, Research in Number Theory, 3:16 (2017).
  3. A database of number fields, with D. Roberts, LMS J. Comput. Math., 17, 595-618 (2014). (arxiv version)
  4. The tame-wild principle for discriminant relations for number fields, with D. Roberts, Algebra and Number Theory, 8 no. 3, 609-645 (2014).
  5. Minimal solvable nonic fields, LMS J. Comput. Math., 16, 130-138 (2013).
  6. Number fields with solvable Galois groups and small Galois root discriminants, with R. Wallington, Math. Comp., 81, 555-567 (2012).
  7. Wild ramification bounds and simple group Galois extensions ramified only at 2, Proc. Amer. Math. Soc., 139, 807-821 (2011).
  8. Minimum discriminants of imprimitive decic fields, with E. Driver, Exp. Math., 19, 475-479 (2010).
  9. Number fields unramified away from 2, J. Number Theory, 130, 1282-1291 (2010).
  10. Inertia subgroups for octic 2-adic fields, Int. J. Pure Appl. Math., 61, 301-314 (2010).
  11. A targeted Martinet search, with E. Driver, Math. Comp., 78, 1109-1117 (2009).
  12. $\mathbf{Z}$-cyclic whist tournaments for $q^2$ players, with P. Leonard, J. Combin. Math. Combin. Comput., 66, 215-223 (2008).
  13. Octic 2-adic fields, with D. Roberts, J. Number Theory, 128, 1410-1429 (2008).
  14. Number fields ramified at one prime, with D. Roberts, in ANTS VIII, Springer Lecture Notes in Computer Science, 5011, 226-239 (2008).
  15. Galois number fields with small root discriminant, with D. Roberts, J. Number Theory, 122, 379-407 (2007).
  16. A database of local fields, with D. Roberts, J. Symbolic Comput., 41, 80-97 (2006).
  17. Nonic 3-adic fields, with D. Roberts, in ANTS VI, Springer Lecture Notes in Computer Science, 3076, 293-308 (2004).
    A revision correcting an error in the published version.
  18. Septic fields with discriminant $\pm 2^a 3^b$, with D. Roberts, Math Comp., 72, 1975-1985, (2003).
  19. Sextic number fields with discriminant $ (-1)^j 2^a 3^b$ , with D. Roberts, in Number Theory: Fifth Conference of the Canadian Number Theory Association, CRM Proceedings and Lecture Notes, 19, American Math. Soc., 141-172 (1999).
  20. Timing analysis of targeted Hunter searches, with D. Roberts, in ANTS III, Springer Lecture Notes in Computer Science, 1423, 412-423 (1998).
  21. Zero free regions for a rational function with applications, with B. Welfert, Advances in Computational Mathematics, 3, 265-289 (1995).
  22. Plater's $p$-adic orthogonality relation for abelian varieties, Houston J. Math., 21, 261-282 (1995).
  23. Iwasawa $L$-functions of elliptic curves with additive reduction, J. Number Theory, 51, 103-117 (1995).
  24. On the equation $x^4+mx^2y^2+y^4=z^2$, with A. Bremner, J. Number Theory, 50, 286-298 (1995).
  25. Iwasawa L-functions and the mysterious $\cal L$-invariant, in p-adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, AMS Contemporary Math Series 165, 63-70 (1994).
  26. On the local norm map for abelian varieties with good ordinary reduction, J. Algebra 138, 420-423 (1991).
  27. A comparison of Selmer groups, Manuscripta Math. 68, 391-398 (1990).
  28. $p$-adic heights for semi-stable abelian varieties, Compositio Math. 73, 31-56 (1990).
  29. Iwasawa $L$-functions for multiplicative abelian varieties, Duke Math. J. 59, 399-420 (1989).

Books

  1. Discovering Number Theory, with J. Holt, W.H. Freeman and Company, New York (2001).
  2. Instructor's Manual for Discovering Number Theory cd-rom, with J. Holt, W.H. Freeman and Company, New York (2001).
  3. Arithmetic Geometry: Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, March 15-18, 1993 at Arizona State University, coeditor with N. Childress, AMS Contemporary Math. Series, 174, (1994).

Pedagogy Articles

  1. Looking at Groups, Res. J. Math. Technol., 1, 111-120 (2012). Also published in Elec. J. Math. Technol., 6, 1933-2823 (2012).
  2. Teaching Number Theory with CAS or Java, with J. Holt, Proceedings for the 11th Annual International Conference on Technology in Collegiate Mathematics, 178-182, (1999).
  3. Discovering Number Theory, with J. Holt. Proceedings for the 10th Annual International Conference on Technology in Collegiate Mathematics, 211-215, (1998).
Last Update: July 10, 2017

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