PAPERS
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
Idoneal numbers vs fundamental discriminants PDF
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. Some remarks on Heegner point computations Postscript PDF
10. A note on integral points on elliptic curves Postscript PDF
11. Symmetric power L-functions of elliptic curves Postscript PDF
(Joint with Phil Martin)
12. Some heuristics about elliptic curves Postscript PDF
13. Critical values of symmetric power $L$-functions Postscript PDF
(Joint with Neil Dummigan)
14. Root numbers of symmetric powers Postscript PDF
(Joint with Neil Dummigan and Phil Martin)
15. On elliptic curves and random matrix theory Postscript PDF
16. On the Extremality of an 80-Dimensional Lattice Postscript PDF
(Joint with Damien Stehle)
17. Computing with Hecke Grossencharacters Postscript PDF
18. Another 80-dimensional extremal lattice PDF
19. Some comments about Indefinite LLL PDF
20. Ranks of quadratic twists of the congruent number curve PDF
(With Steve Donnelly, Noam Elkies, Tom Fisher, Andrew Granville, and Nick Rogers)
21. Jacobi sum motives and Grossencharacters PDF
22. Class number one from analytic rank two PDF
23. A spectral proof of class number one PDF
24a. A new effective lower bound on L_\chi(1) PDF
24b. Computing L_E'''(1) to high precision PDF
24c. On Chowla's conjecture for Q(\sqrt{4u^2+1}) PDF
24a/24c have been re-combined (making many corrections) into a different paper:
Class number problems for real quadratic fields PDF
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EXPOSITORY PAPERS AND SHORT NOTES
Explicit lower bounds on the modular degree of an elliptic curve Postscript 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
Hypergeometric motives notes PDF
Also the Magma handbook chapter PDF
Discursus on rank 21 PDF
Comments on Deuring's zero-spacing phenomenon PDF
Discretisation for odd quadratic twists Postscript PDF
(Joint with J. Brian Conrey, Michael O. Rubinstein, and Nina C. Snaith)
The power of logarithm for quadratic twists Postscript PDF
(Joint with Christophe Delaunay)
Two new proofs of class number one (Oberwolfach abstract 2018) PDF
Distribution of the 2-Selmer rank after twisting (apres Smith) PDF
Notes on 4-Selmer and 8-class ranks PDF
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PAPERS ON COMPUTER CHESS
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