1. Computing the modular degree of an elliptic curve Postscript PDF

2. Resolution of class number 100 for imaginary quadratic fields Postscript PDF

List of fundamental discriminants here

3. Real zeros of real odd Dirichlet L-functions Postscript PDF

4. A database of elliptic curves---first report Postscript PDF
(Joint with William A. Stein)

5. Constructing elements in Shafarevich-Tate groups of modular motives PS PDF
(Joint with Neil P. Dummigan and William A. Stein)

6. Rank distribution in a family of cubic twists Postscript PDF

7. Elliptic curves of large rank and small conductor Postscript PDF
(Joint with Noam D. Elkies)

8. Modular Parametrizations of Neumann--Setzer Elliptic Curves Postscript PDF
(Joint with William A. Stein)

9. Explicit lower bounds on the modular degree of an elliptic curve Postscript PDF

10. Some remarks on Heegner point computations Postscript PDF

11. A note on integral points on elliptic curves Postscript PDF

12. Discretisation for odd quadratic twists Postscript PDF
(Joint with J. Brian Conrey, Michael O. Rubinstein, and Nina C. Snaith)

13. The power of logarithm for quadratic twists Postscript PDF
(Joint with Christophe Delaunay)

14. Symmetric power L-functions of elliptic curves Postscript PDF
(Joint with Phil Martin)

15. Average Ranks of Elliptic Curves External Link
(Joint with Baur Bektemirov, Barry Mazur, and William Stein)

16. Some heuristics about elliptic curves Postscript PDF

17. Critical values of symmetric power $L$-functions Postscript PDF
(Joint with Neil Dummigan)

18. Root numbers of symmetric powers Postscript PDF
(Joint with Neil Dummigan and Phil Martin)

19. On elliptic curves and random matrix theory Postscript PDF

20. On the Extremality of an 80-Dimensional Lattice Postscript PDF
(Joint with Damien Stehle)

21. Computing with Hecke Grossencharacters Postscript PDF

22. Another 80-dimensional extremal lattice PDF

23. Some comments about Indefinite LLL PDF

24. Ranks of quadratic twists of the congruent number curve PDF
(With Steve Donnelly, Noam Elkies, Tom Fisher, Andrew Granville, and Nick Rogers)

25. Hypergeometric motives notes PDF
Also the Magma handbook chapter PDF

26. Jacobi sum motives and Grossencharacters PDF


The Green-Tao Theorem Postscript PDF

On Sums of Four Cubes Postscript PDF

Note on the Chowla conjecture Postscript PDF

Notes from a class on sieves Postscript PDF

Notes from talks about the work of Connes Postscript PDF

Discursus on rank 21 PDF

Comments on the Deuring-Heilbronn phenomenon PDF

IN PROGRESS (or reached a deadend)

Isogenies of Elliptic Curves Postscript
(Joint with John E. Cremona)

Polynomial Families and the Davenport-Mason bound Postscript
(Joint with Noam D. Elkies)

Searching for points p-adically Postscript


Move similarity analysis in chess programs PDF
(Joint with Don Dailey and Adam Hair)

Solved openings in Losing Chess PDF

Losing Chess: 1. e3 wins for White PDF

Recap of the Rybka case PDF (Expository)