Throughout this paper d will denote a fundamental discriminant, and χd the associated primitive real character to the modulus |d|. We investigate here the distribution of values of L(1, χd) as d… (More)

We investigate integer solutions of the superelliptic equation (1) z = F (x, y), where F is a homogenous polynomial with integer coefficients, and of the generalized Fermat equation (2) Ax + By = Cz,… (More)

The analysis of many number theoretic algorithms turns on the role played by integers which have only small prime factors; such integers are known as “smooth numbers”. To be able to determine which… (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of… (More)

After the first world war, Cramér began studying the distribution of prime numbers, guided by Riesz and Mittag-Leffler. His works then, and later in the midthirties, have had a profound influence on… (More)

In the 80’s Maier showed that the primes cannot be distributed too evenly in short intervals. This was subsequently refined and extended to the distribution of primes in arithmetic progressions by… (More)

We classify those finite simple groups whose Brauer graph (or decomposition matrix) has a p-block with defect 0, completing an investigation of many authors. The only finite simple groups whose… (More)

Erdős conjectured that there are x1−o(1) Carmichael numbers up to x, whereas Shanks was skeptical as to whether one might even find an x up to which there are more than √ x Carmichael numbers.… (More)

There has been no subsequent improvement in this inequality other than in the implicit constant. Moreover it is believed that (1.1) will be difficult to improve since it is possible (though highly… (More)