Prime covers and periodic patterns

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Cyclic Covers of Prime Power Degree, Jacobians and Endomorphisms

Suppose K is a field of characteristic zero, Ka is its algebraic closure, f(x) ∈ K[x] is an irreducible polynomial of degree n ≥ 5, whose Galois group coincides either with the full symmetric group Sn or with the alternating group An. Let q be a power prime, Pq(t) = t q −1 t−1 . Let C be the superelliptic curve y = f(x) and J(C) its jacobian. We prove that if p does not divide n then the algebr...

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Juggling patterns can be described by a closed walk in a (directed) state graph, where each vertex (or state) is a landing pattern for the balls and directed edges connect states that can occur consecutively. The number of such patterns of length n is well known, but a long-standing problem is to count the number of prime juggling patterns (those juggling patterns corresponding to cycles in the...

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To Paulo Ribenboim and his friends, the primes. 1. INTRODUCTION. It has long been known that there are infinitely many primes, and that there are infinitely many primes in any arithmetic progression a, a + d, a + 2d,. .. provided gcd(a, d) = 1 and d ≥ 1. If we ask slightly more involved questions, such as whether there exist infinitely many primes of the form n

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The first records of studies of prime numbers come from the Ancient Greeks. Euclid proved that there are an infinite number of primes as well as the Fundamental Theorem of Arithmetic which states that every natural number greater than 1 can be written as a unique product of prime numbers. Since the Greeks, prime numbers have been found to apply to more than just pure mathematics, but have appli...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 1990

ISSN: 0012-365X

DOI: 10.1016/0012-365x(90)90021-9