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Non-abelian number fields with very large class numbers
1.1. Background and motivation. Let K be a number field and denote by H its group of ideal classes. Since H is finite an interesting question one may ask is how its size, the class number of K,Expand
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Maximal Class Numbers of CM Number Fields
Fix a totally real number eld F of degree at least 2. Under the assumptions of the generalized Riemann hypothesis and Artin’s conjecture on the entirety of Artin L-functions, we derive an upper boundExpand
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Budding Yeast, Branching Processes, and Generalized Fibonacci Numbers
Summary An application of branching processes to a problem in cell biology is described, in which the generalized Fibonacci numbers known as k-nacci numbers play a crucial role. The k-nacci sequenceExpand
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Algebraic integers on the unit circle
Abstract By computing the rank of the group of unimodular units in a given number field, we provide a simple proof of the classification of the number fields containing algebraic integers of modulusExpand
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The Chinese Remainder Theorem
Clearly x = 8 is a solution. If y were another solution, then we would have y ≡ 8(mod 5) and y ≡ 8(mod 6). Hence 5|y − 8 and 6|y − 8. As (5, 6) = 1, this means 30|y − 8 or y ≡ 8 (mod 30). As thisExpand
On primitivity of Dirichlet characters
Recall that a Dirichlet character is called imprimitive if it is induced from a character of smaller level, and otherwise it is called primitive. In this paper, we introduce a modification ofExpand
On the counting function for the generalized Niven numbers
Etant donnes q ≥ 2 un entier naturel et f une fonction completement q-additive a valeurs dans l'ensemble des nombres entiers relatifs, on calcule une expression asymptotique de la fonction N f qui aExpand
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Efficient Modular Exponentiation
Muller’s Ratchet in Asexual Populations Doomed to Extinction
Asexual populations are expected to accumulate deleterious mutations through a process known as Muller’s Ratchet. Lynch, Gabriel, and colleagues have proposed that the Ratchet eventually results in aExpand
The Structure of ( Z / n Z ) ×
(below we will define such a function to be a group ismorphism). This reduces the study of the general unit group (Z/nZ)× to understanding the unit group (Z/pnZ)× with prime power modulus. It turnsExpand