A Banach space determined by the Weil height
A Bound for the Least Prime Ideal in the Chebotarev Density Theorem.
A bound for the torsion in the -theory of algebraic integers.
A categorical contribution to the Kummer theory of ideal numbers
A certain property of polynomials.
A certain property of polynomials. (Short Communication).
A Characterization of Algebraic Number Fields with Cyclic Class Group of Prime Power Order.
A characterization of Hermitian function fields over finite fields.
A “class group” obstruction for the equation
In this paper, we study equations of the form , where is a binary form, homogeneous of degree , which is supposed to be primitive and irreducible, and is any fixed integer. Using classical tools in algebraic number theory, we prove that the existence of a proper solution for this equation implies the existence of an integral ideal of given norm in some order in a number field, and also the existence of a specific relation in the class group involving this ideal. In some cases, this result...
A class number congruence for cyclotomic fields and their subfields
A class number criterion for the equation
A class of diophantine equations connected with certain elliptic curves over
A Class of Discrete Spectra of Non-Pisot Numbers
A class of irreducible polynomials
Let , where . We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of on the coefficients of f(x) is the best possible in this situation.
A Class of Periodic Jacobi-Perron Algorithms in Pure Algebraic Number Fields of Degree n...3.
A class of polynomials
A class–field theoretical calculation
In this paper, we give the complete characterization of the –torsion subgroups of certain idèle–class groups associated to characteristic function fields. As an application, we answer a question which arose in the context of Tan’s approach [6] to an important particular case of a generalization of a conjecture of Gross [4] on special values of –functions.
A combinatorial class number formula.
A combinatorial interpretation of Serre's conjecture on modular Galois representations
We state a conjecture concerning modular absolutely irreducible odd 2-dimensional representations of the absolute Galois group over finite fields which is purely combinatorial (without using modular forms) and proof that it is equivalent to Serre’s strong conjecture. The main idea is to replace modular forms with coefficients in a finite field of characteristic , by their counterparts in the theory of modular symbols.
A comparison of elliptic units in certain prime power conductor cases
The aim of this paper is to compare two modules of elliptic units, which arise in the study of elliptic curves E over quadratic imaginary fields K with complex multiplication by , good ordinary reduction above a split prime p and prime power conductor (over K). One of the modules is a special case of those modules of elliptic units studied by K. Rubin in his paper [Invent. Math. 103 (1991)] on the two-variable main conjecture (without p-adic L-functions), and the other module is a smaller one,...