Publications: Publications:

Space vectors forming rational angles, with Kiran S. Kedlaya, Alexander Kolpakov, Bjorn Poonen, submitted.

The South Caicos Factoring Algorithm, accepted by Integers.

Mixed moments of characteristic polynomials of random unitary matrices, with Emma C. Bailey, Sandro Bettin, Gordon Blower, J. Brian Conrey, Andrei Prokhorov, Nina C. Snaith, Journal of Math. Phys., 60, (2019).

Some multidimensional integrals in number theory and connections with the Painlevé V equation, with Estelle Basor, Fan Ge, J. Math. Phys., 59, (2018).

Riemann's influence in number theory from a computational and experimental perspective, Advanced Lectures in Mathematics, 35 (2016), 633-680.

Moments of zeta functions associated to hyperelliptic curves over finite fields, with K. Wu, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 373 (2015), no. 2040.

The highest lowest zero of general L-functions with Jonathan Bober, J. Brian Conrey, David W. Farmer, Akio Fujii, Sally Koutsoliotas, Stefan Lemurell, Hiroyuki Yoshida, Journal of Number Theory 147 (2015), 364–373.

Computing the moment polynomials of the zeta function , with S. Yamagishi, Mathematics of Computation 84 (2015), 425-454.

Elliptic curves of high rank and the Riemann zeta function Experimental Mathematics, Volume 22, No. 4 (2013), 465-480.

Identities for the Hurwitz zeta function, Gamma function, and L-functions, Ramanujan Journal, Volume 32, Issue 3 (2013), 421--464.

Chebotarev sets , with H. Kisilevsky, Acta Arithmetica 171 (2015), 97-124.

Lower order terms for the moments of symplectic and orthogonal families of L-functions , with I.P. Goulden, D.K. Huynh, and Rishikesh, Journal of Number Theory, Volume 133, Issue 2, February 2013, 639--674.

The distribution of solutions to XY=N mod a with an application to factoring integers, Integers, 13 (2013), A12, 1--13.

Conjectures and experiments concerning the moments of L(1/2,chi_d) with M. Alderson, Experimental Mathematics, Volume 21, Issue 3 (2012), 307-328.

Uniform asymptotics for the full moment conjecture of the Riemann zeta function , with G.A. Hiary, Journal of Number Theory, Volume 132, Issue 4, (2012), 820-868.

Uniform asymptotics of the coefficients of unitary moment polynomials , with G.A. Hiary, Proceedings of the Royal Soc. A, April 8, 2011 467:1073-1100.

Some identities for the Riemann zeta function, Ramanujan Journal. Volume 27, Issue 1 (2012), pp 29-42.

Lower order terms in the full moment conjecture for the Riemann zeta function , with J.B. Conrey, D. Farmer, J.P. Keating, and N.C. Snaith, Journal of Number Theory, Volume 128, Issue 6, June 2008, 1516-1554.

Discretisation for odd quadratic twists , with J.B. Conrey, N.C. Snaith, and M. Watkins, Proceedings of Ranks of Elliptic Curves and Random Matrix, Cambridge University Press, 2007.

Secondary terms in the number of vanishings of quadratic twists of elliptic curve L-functions , with J.B. Conrey, A. Pokharel, and M. Watkins, Proceedings of Ranks of Elliptic Curves and Random Matrix, Cambridge University Press, 2007.

Moments of the derivative of the Riemann zeta-function and of characteristic polynomials , with J.B. Conrey, and N.C. Snaith, Communications in Mathematical Physics, 267 (2006), no. 3, 611-629.

Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms , with J.B. Conrey, J.P. Keating, and N.C. Snaith, Experimental Mathematics, 15 (2006), no. 1.

Computational methods and experiments in analytic number theory, In: Recent Perspectives in Random Matrix Theory and Number Theory, F. Mezzadri and N.C. Snaith editors, 407-483, 2005. High resolution version of the Figure 6 in the paper: compressed postscript.

Integral moments of L-functions, with B. Conrey, D. Farmer, J.P. Keating, and N.C. Snaith. Proceedings of the London Mathematical Society (3) 91 (2005), 33-104.

Autocorrelation of Random Matrix Polynomials, with B. Conrey, D. Farmer, J.P. Keating, and N.C. Snaith. Communications in Mathematical Physics 237 (2003), no.3, 365-395.

On the frequency of vanishing of quadratic twists of modular L-functions, with J.B. Conrey, J.P. Keating, and N.C. Snaith. Proceedings of the Millenium Number Theory Conference, editor, B.C. Berndt et al A.K. Peters, Ltd, Boston, 1 (2001) 301-316.

Low lying zeros of L-functions and random matrix theory. Duke Mathematical Journal 109 (2001), no. 1, 147-181.

Zeros of Dirichlet L-functions near the real axis and Chebyshev's bias, with Carter Bays, Kevin Ford, Richard Hudson. Journal of Number Theory 87 (2001), no. 1, 54-76.

Jumping champions, with Andrew Odlyzko, and Marek Wolf. Experimental Mathematics 8 (1999), no. 2, 107-118.

On the computation of modular polynomials for elliptic curvess, Ian Blake, Janos Csirik, and Gadiel Seroussi, Hewlett-Packard Laboratories technical report, 1999.

Evidence for a spectral interpretation of the zeros of L-functions. Princeton Ph.D. thesis, June 1998.

The number of intersection points made by the diagonals of a regular polygon, with Bjorn Poonen. SIAM Journal on Discrete Mathematics 11 (1998), no. 1, 135-156.

On a conjecture of Helleseth regarding pairs of binary m-sequences, with A.R. Calderbank, Gary McGuire, and Bjorn Poonen. IEEE Transactions on Information Theory 42 (1996), no. 3, 988-990.

Chebyshev's bias, with Peter Sarnak. Experimental Mathematics 3 (1994), no. 3, 173-197.

A simple heuristic proof of Hardy and Littlewood's conjecture B, American Mathematical Monthly 100 (1993), no. 5, 456-460.

A formula and a proof of the infinitude of primes, American Mathematical Monthly 100 (1993), no. 4, 388-392.

The conditional convergence of the Dirichlet series of an L-function