The square of the Fermat quotient.
Cycle lengths in a permutation are typically Poisson.
Borwein and Bradley's Apéry-like formulae for .
Product of integers in an interval, modulo squares.
Bounding the Coefficients of a Divisor of a Given Polynomial.
The lattice points of an n-dimensional tetrahedron. (Summary).
On Krasner's Criteria for the First Case of Fermat's Last Theorem.
The lattice points of an n-dimensional tetrahedron.
Finding integers k for which a given Diophantine equation has no solution in kth powers of integers
Primitive prime factors in second-order linear recurrence sequences
Solution to a problem of Bombieri
We solve a problem of Bombieri, stated in connection with the «prime number theorem» for function fields.
Recenze pořadu Horizon stanice BBC „Fermatova poslední věta‟
Pretentiousness in analytic number theory
In this report, prepared specially for the program of the , we describe how, in joint work with K. Soundararajan and Antal Balog, we have developed the notion of “pretentiousness” to help us better understand several key questions in analytic number theory.
Limitations to the equi-distribution of primes III
On Sophie Germain type criteria for Fermat's Last Theorem
The number of unsieved integers up to x
Rabinowitsch revisited
Zeros of Fekete polynomials
For an odd prime, we show that the Fekete polynomial has zeros on the unit circle, where . Here is the probability that the function has a zero in , where each is with y . In fact has absolute value at each primitive th root of unity, and we show that if for some then there is a zero of close to this arc.
Ranks of quadratic twists of elliptic curves
We report on a large-scale project to investigate the ranks of elliptic curves in a quadratic twist family, focussing on the congruent number curve. Our methods to exclude candidate curves include 2-Selmer, 4-Selmer, and 8-Selmer tests, the use of the Guinand-Weil explicit formula, and even 3-descent in a couple of cases. We find that rank 6 quadratic twists are reasonably common (though still quite difficult to find), while rank 7 twists seem much more rare. We also describe our inability to find...
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