John Jones - Publications

Papers

1. Inertia subgroups for octic 2-adic fields, submitted.
2. A targeted Martinet search, with E. Driver, submitted.
3. Number fields unramified away from 2, submitted.
4. Octic 2-adic Fields, with D. Roberts, to appear J. Number Theory.
5. Number fields ramified at one prime, with D. Roberts, to appear in ANTS VIII, Springer Lecture Notes in Computer Science.
6. Z-cyclic whist tournaments for q² players, with P. Leonard, to appear in JCMCC.
7. Galois Number Fields with Small Root Discriminant, with D. Roberts, J. Number Theory, 122, 379-407 (2007).
8. A Database of Local Fields, with D. Roberts, J. Symbolic Comput., 41, 80-97 (2006).
9. 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.
10. Septic Fields with Discriminant ± 2^a 3^b, with D. Roberts, Math Comp., 72, 1975-1985, (2003).
11. 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).
12. Timing Analysis of Targeted Hunter Searches, with D. Roberts, in ANTS III, Springer Lecture Notes in Computer Science, 1423, 412-423 (1998).
13. Zero free regions for a rational function with applications, with B. Welfert, Advances in Computational Mathematics, 3, 265-289 (1995).
14. Plater's p-adic orthogonality relation for Abelian varieties, Houston J. Math., 21, 261-282 (1995).
15. Iwasawa L-functions of elliptic curves with additive reduction, J. Number Theory, 51, 103-117 (1995).
16. On the equation $x^4+mx^2y^2+y^4=z^2$, with A. Bremner, J. Number Theory, 50, 286-298 (1995).
17. 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).
18. On the local norm map for abelian varieties with good ordinary reduction, J. Algebra 138, 420-423 (1991).
19. A comparison of Selmer groups, Manuscripta Math. 68, 391-398 (1990).
20. p-adic heights for semi-stable abelian varieties, Compositio Math. 73, 31-56 (1990).
21. 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. Discovering Number Theory, with J. Holt. Proceedings for the 10th Annual International Conference on Technology in Collegiate Mathematics, 211-215, (1998).
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).