The Class Number of Hereditary Orders in Non-Eichler Algebras over Global Fuction Fields.
The class number of pairs of positive-definite binary quadratic forms
The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer
The class number one problem for some non-abelian normal CM-fields of degree
We determine all the non-abelian normal CM-fields of degree 24 with class number one, provided that the Galois group of their maximal real subfields is isomorphic to , the alternating group of degree and order . There are two such fields with Galois group (see Theorem 14) and at most one with Galois group SL (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number .
The class number one problem for the dihedral and dicyclic CM-fields
We recall the determination of all the dihedral CM-fields with relative class number one, and prove that dicyclic CM-fields have relative class numbers greater than one.
The class number one problem for the non-abelian normal CM-fields of degree 16
The class number one problem for the non-abelian normal CM-fields of degree 24 and 40
The class number one problem for the non-normal sextic CM-fields. Part 2
The class number one problem for the real quadratic fields ℚ(√((an)²+4a))
We solve unconditionally the class number one problem for the 2-parameter family of real quadratic fields ℚ(√d) with square-free discriminant d = (an)²+4a for positive odd integers a and n.
The class of Erdős-Turán sets
The classification of (3, 3, 3) trilinear forms.
The classification of pairs of binary quadratic forms
The classification of modular invariants revisited
The closures of arithmetic progressions in the common division topology on the set of positive integers
In this paper we characterize the closures of arithmetic progressions in the topology T on the set of positive integers with the base consisting of arithmetic progressions {an + b} such that if the prime number p is a factor of a, then it is also a factor of b. The topology T is called the common division topology.
The Coefficients of Cosh x/cos x.
The Cohen-Lenstra heuristics, moments and -ranks of some groups
This article deals with the coherence of the model given by the Cohen-Lenstra heuristic philosophy for class groups and also for their generalizations to Tate-Shafarevich groups. More precisely, our first goal is to extend a previous result due to É. Fouvry and J. Klüners which proves that a conjecture provided by the Cohen-Lenstra philosophy implies another such conjecture. As a consequence of our work, we can deduce, for example, a conjecture for the probability laws of -ranks of Selmer groups...
The Collatz problem and analogues.
The combinatorialization of linear recurrences.
The combinatorics of certain -ary meta-Fibonacci sequences.
The common division topology on
A topological space is totally Brown if for each and every nonempty open subsets of we have . Totally Brown spaces are connected. In this paper we consider a topology on the set of natural numbers. We then present properties of the topological space , some of them involve the closure of a set with respect to this topology, while others describe subsets which are either totally Brown or totally separated. Our theorems generalize results proved by P. Szczuka in 2013, 2014, 2016 and by...