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**publisher and metadata sources**).For an imaginary quadratic number field K and an odd prime number l, the anti-cyclotomic Z l -extension of K is defined. For primes p of K, decomposition laws for p in the anti-cyclotomic extension… Continue Reading

The minimal number of spheres (without ”interior”) of radius n required to cover the finite set {0, . . . , q−1}n equipped with the Hamming distance is denoted by T (n, q). The only hitherto known… Continue Reading

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It is a theorem of Kaplansky that a prime p≡1(mod16) is representable by both or none of x2+32y2 and x2+64y2, whereas a prime p≡9(mod16) is representable by exactly one of these binary… Continue Reading

In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X2+nY2. Based on some numerical… Continue Reading

First, a generalization of Chevalley’s classical theorem from 1936 on polynomial equations f(x1,...,xN) = 0 over a finite field K is given, where the variables xi are restricted to arbitrary subsets… Continue Reading

Given a year with n≥1 days, the Birthday Problem asks for the minimal number such that in a class of students, the probability of finding two students with the same birthday is at least 50 percent.… Continue Reading

Adequate pretreatment including fine screening is essential to the stable, long-term operation of membrane bioreactors (MBR) used to treat municipal wastewater. The amount of screenings generated by… Continue Reading

Fix an integern≧3. We show that the alternating groupAn appears as Galois group over any Hilbertian field of characteristic different from 2. In characteristic 2, we prove the same whenn is odd. We… Continue Reading