## Currently displaying 1 – 19 of 19

Showing per page

Order by Relevance | Title | Year of publication

### Bounding the Coefficients of a Divisor of a Given Polynomial.

Monatshefte für Mathematik

### The lattice points of an n-dimensional tetrahedron. (Summary).

Aequationes mathematicae

### On Krasner's Criteria for the First Case of Fermat's Last Theorem.

Manuscripta mathematica

### The lattice points of an n-dimensional tetrahedron.

Aequationes mathematicae

Acta Arithmetica

Acta Arithmetica

### Solution to a problem of Bombieri

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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‟

Pokroky matematiky, fyziky a astronomie

### Pretentiousness in analytic number theory

Journal de Théorie des Nombres de Bordeaux

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.

Acta Arithmetica

Integers

### Cycle lengths in a permutation are typically Poisson.

The Electronic Journal of Combinatorics [electronic only]

### Zeros of Fekete polynomials

Annales de l'institut Fourier

For $p$ an odd prime, we show that the Fekete polynomial ${f}_{p}\left(t\right)={\sum }_{a=0}^{p-1}\left(\frac{a}{p}\right){t}^{a}$ has $\sim {\kappa }_{0}p$ zeros on the unit circle, where $0.500813>{\kappa }_{0}>0.500668$. Here ${\kappa }_{0}-1/2$ is the probability that the function $1/x+1/\left(1-x\right)+{\sum }_{n\in ℤ:\phantom{\rule{4pt}{0ex}}n\ne 0,1}{\delta }_{n}/\left(x-n\right)$ has a zero in $\right]0,1\left[$, where each ${\delta }_{n}$ is $±1$ with y $1/2$. In fact ${f}_{p}\left(t\right)$ has absolute value $\sqrt{p}$ at each primitive $p$th root of unity, and we show that if $|{f}_{p}\left(e\left(2i\pi \left(K+\tau \right)/p\right)\right)|<ϵ\sqrt{p}$ for some $\tau \in \right]0,1\left[$ then there is a zero of $f$ close to this arc.

### Ranks of quadratic twists of elliptic curves

Publications mathématiques de Besançon

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...

### Borwein and Bradley's Apéry-like formulae for $\zeta \left(4n+3\right)$.

Experimental Mathematics

### Product of integers in an interval, modulo squares.

The Electronic Journal of Combinatorics [electronic only]

Page 1