Dr Mark Watkins

F07 - Carslaw Building
The University of Sydney

Telephone 9351 5778
Fax 9351 4534

Research interests

Mark Watkins is a member of the Computational Algebra Research Group.

Selected publications

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Book Chapters

  • Watkins, M. (2012). Some remarks on Heegner point computations. In - (Eds.), Explicit Methods in Number Theory, (pp. 81-97). France: Societe Mathematique de France.

Journals

  • Watkins, M. (2019). A spectral proof of class number one. Mathematische Zeitschrift, In Press. [More Information]
  • Watkins, M. (2019). Class number one from analytic rank two. Mathematika, 65(2), 333-374. [More Information]
  • Watkins, M. (2018). Jacobi sums and Grossencharacters. Publications Mathematiques de Besancon, 2018, 111-122. [More Information]
  • Watkins, M. (2017). Losing Chess: 1. E3 Wins for White. ICGA Journal, 39(2), 123-125. [More Information]
  • Dailey, D., Hair, A., Watkins, M. (2014). Move similarity analysis in chess programs. Entertainment Computing, 5(3), 159-171. [More Information]
  • Watkins, M., Donnelly, S., Elkies, N., Fisher, T., Granville, A., Rogers, N. (2014). Ranks of quadratic twists of elliptic curves. Publications Mathematiques de Besancon, 2014 (2), 63-98. [More Information]
  • Watkins, M. (2014). Solved Openings in Losing Chess. ICGA Journal, 37(2), 106-110. [More Information]
  • Watkins, M. (2012). Another 80-dimensional extremal lattice. Journal de Theorie des Nombres de Bordeaux, 24(1), 237-255. [More Information]
  • Watkins, M. (2011). Computing with Hecke Grossencharacters. Publications Mathematiques de Besancon, 2011, 119-135.
  • Cannon, J., Donnelly, S., Fieker, C., Watkins, M. (2010). Magma - a tool for number theory. Lecture Notes in Computer Science (LNCS), 6327, 253-255. [More Information]
  • Dummigan, N., Watkins, M. (2009). Critical values of symmetric power L-functions. Pure and Applied Mathematics Quarterly, 5(1), 127-161. [More Information]
  • Dummigan, N., Martin, P., Watkins, M. (2009). Euler factors and local root numbers for symmetric powers of elliptic curves. Pure and Applied Mathematics Quarterly, 5(4), 1311-1341. [More Information]
  • Watkins, M. (2008). On elliptic curves and random matrix theory. Journal de Theorie des Nombres de Bordeaux, 20(3), 829-845. [More Information]
  • Watkins, M. (2008). Some heuristics about elliptic curves. Experimental Mathematics, 17(1), 105-125. [More Information]
  • Watkins, M. (2006). A note on integral points on elliptic curves. Journal de Theorie des Nombres de Bordeaux, 18(3), 707-720.
  • Watkins, M. (2004). Class numbers of imaginary quadratic fields. Mathematics of Computation, 73(246), 907-938. [More Information]
  • Elkies, N., Watkins, M. (2004). Elliptic Curves of Large Rank and Small Conductor. Lecture Notes in Computer Science (LNCS), LNCS 3076(-), 42-56.
  • Stein, W., Watkins, M. (2004). Modular parametrizations of Neumann-Setzer elliptic curves. International Mathematics Research Notices, 27(-), 1395-1405.
  • Watkins, M. (2004). Real zeros of real odd dirichlet L-functions. Mathematics of Computation, 73(245), 415-423. [More Information]

Conferences

  • Watkins, M. (2013). Some Comments about Indefinite LLL. Diophantine Methods, Lattics, and Arithmetic Theory of Quadratic Forms, USA: AMS Press, Inc.
  • Hart, W., Tornaria, G., Watkins, M. (2010). Congruent Number Theta Coefficients to 10^12. 9th International Symposium on Algorithmic Number Theory, ANTS-IX 2010, Berlin Heidelberg: Springer. [More Information]
  • Stehle, D., Watkins, M. (2010). On the Extremality of an 80-Dimensional Lattice. 9th International Symposium on Algorithmic Number Theory, ANTS-IX 2010, Berlin Heidelberg: Springer. [More Information]
  • Watkins, M., Martin, P. (2006). Symmetric Powers of Elliptic Curve L-Functions. 7th Algorithmic Number Theory International Symposium, ANTS VII (2006), Berlin Heidelberg New York: Springer.

2019

  • Watkins, M. (2019). A spectral proof of class number one. Mathematische Zeitschrift, In Press. [More Information]
  • Watkins, M. (2019). Class number one from analytic rank two. Mathematika, 65(2), 333-374. [More Information]

2018

  • Watkins, M. (2018). Jacobi sums and Grossencharacters. Publications Mathematiques de Besancon, 2018, 111-122. [More Information]

2017

  • Watkins, M. (2017). Losing Chess: 1. E3 Wins for White. ICGA Journal, 39(2), 123-125. [More Information]

2014

  • Dailey, D., Hair, A., Watkins, M. (2014). Move similarity analysis in chess programs. Entertainment Computing, 5(3), 159-171. [More Information]
  • Watkins, M., Donnelly, S., Elkies, N., Fisher, T., Granville, A., Rogers, N. (2014). Ranks of quadratic twists of elliptic curves. Publications Mathematiques de Besancon, 2014 (2), 63-98. [More Information]
  • Watkins, M. (2014). Solved Openings in Losing Chess. ICGA Journal, 37(2), 106-110. [More Information]

2013

  • Watkins, M. (2013). Some Comments about Indefinite LLL. Diophantine Methods, Lattics, and Arithmetic Theory of Quadratic Forms, USA: AMS Press, Inc.

2012

  • Watkins, M. (2012). Another 80-dimensional extremal lattice. Journal de Theorie des Nombres de Bordeaux, 24(1), 237-255. [More Information]
  • Watkins, M. (2012). Some remarks on Heegner point computations. In - (Eds.), Explicit Methods in Number Theory, (pp. 81-97). France: Societe Mathematique de France.

2011

  • Watkins, M. (2011). Computing with Hecke Grossencharacters. Publications Mathematiques de Besancon, 2011, 119-135.

2010

  • Hart, W., Tornaria, G., Watkins, M. (2010). Congruent Number Theta Coefficients to 10^12. 9th International Symposium on Algorithmic Number Theory, ANTS-IX 2010, Berlin Heidelberg: Springer. [More Information]
  • Cannon, J., Donnelly, S., Fieker, C., Watkins, M. (2010). Magma - a tool for number theory. Lecture Notes in Computer Science (LNCS), 6327, 253-255. [More Information]
  • Stehle, D., Watkins, M. (2010). On the Extremality of an 80-Dimensional Lattice. 9th International Symposium on Algorithmic Number Theory, ANTS-IX 2010, Berlin Heidelberg: Springer. [More Information]

2009

  • Dummigan, N., Watkins, M. (2009). Critical values of symmetric power L-functions. Pure and Applied Mathematics Quarterly, 5(1), 127-161. [More Information]
  • Dummigan, N., Martin, P., Watkins, M. (2009). Euler factors and local root numbers for symmetric powers of elliptic curves. Pure and Applied Mathematics Quarterly, 5(4), 1311-1341. [More Information]

2008

  • Watkins, M. (2008). On elliptic curves and random matrix theory. Journal de Theorie des Nombres de Bordeaux, 20(3), 829-845. [More Information]
  • Watkins, M. (2008). Some heuristics about elliptic curves. Experimental Mathematics, 17(1), 105-125. [More Information]

2006

  • Watkins, M. (2006). A note on integral points on elliptic curves. Journal de Theorie des Nombres de Bordeaux, 18(3), 707-720.
  • Watkins, M., Martin, P. (2006). Symmetric Powers of Elliptic Curve L-Functions. 7th Algorithmic Number Theory International Symposium, ANTS VII (2006), Berlin Heidelberg New York: Springer.

2004

  • Watkins, M. (2004). Class numbers of imaginary quadratic fields. Mathematics of Computation, 73(246), 907-938. [More Information]
  • Elkies, N., Watkins, M. (2004). Elliptic Curves of Large Rank and Small Conductor. Lecture Notes in Computer Science (LNCS), LNCS 3076(-), 42-56.
  • Stein, W., Watkins, M. (2004). Modular parametrizations of Neumann-Setzer elliptic curves. International Mathematics Research Notices, 27(-), 1395-1405.
  • Watkins, M. (2004). Real zeros of real odd dirichlet L-functions. Mathematics of Computation, 73(245), 415-423. [More Information]

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