On elliptic diophantine equations that defy Thue's method: The case of the Ochoa curve.
On evaluations of infinite double sums and Tornheim's double series.
On Factor Tables, with an Account of the Mode of Formation of the Factor Table for the Fourth Million [Book]
On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function.
On integer sequences associated with the cyclic and complete graphs.
On integers of the form
On normal integral bases in ray class fields over imaginary quadratic fields
On power values of pyramidal numbers, I
On pseudoprimes having special forms and a solution of K. Szymiczek’s problem
We use the properties of -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.
On rational approximations to Euler's constant and to .
On real quadratic number fields suitable for cryptography.
On reduced Arakelov divisors of real quadratic fields
We generalize the concept of reduced Arakelov divisors and define C-reduced divisors for a given number C ≥ 1. These C-reduced divisors have remarkable properties, similar to the properties of reduced ones. We describe an algorithm to test whether an Arakelov divisor of a real quadratic field F is C-reduced in time polynomial in with the discriminant of F. Moreover, we give an example of a cubic field for which our algorithm does not work.
On relative pure cyclic fields with power integral bases
Let be an extension of a number field , where satisfies the monic irreducible polynomial of prime degree belonging to ( is the ring of integers of ). The purpose of this paper is to study the monogenity of over by a simple and practical version of Dedekind’s criterion characterizing the existence of power integral bases over an arbitrary Dedekind ring by using the Gauss valuation and the index ideal. As an illustration, we determine an integral basis of a pure nonic field with a...
On Shanks' algorithm for computing the continued fraction of .
On Shank's algorithm for modular square roots.
On some properties of two simultaneous polygonal sequences.
On some subgroups of the multiplicative group of finite rings
Let be a subset of , the field of elements and a polynomial of degree with no roots in . Consider the group generated by the image of in the group of units of the ring . In this paper we present a number of lower bounds for the size of this group. Our main motivation is an application to the recent polynomial time primality testing algorithm [AKS]. The bounds have also applications to graph theory and to the bounding of the number of rational points on abelian covers of the projective...
On square values of quadratics
On sum-free sequences
On the class numbers of real cyclotomic fields of conductor pq
The class numbers h⁺ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows, and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been developed, which approach the problem from different angles. In this paper we extend one of these methods that was designed for real cyclotomic fields of prime...