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A multidimensional extension of a q-beta integral of Andrews and Askey is evaluated. As an application, a short new proof of an important q-Selberg integral formula is given.
Analogues over finite fields are presented for the major formulas in the theory of classical Hermite functions.
PolC is the polymerase responsible for genome duplication in many Gram-positive bacteria and represents an attractive target for antibacterial development. We have determined the 2.4-A resolution crystal structure of Geobacillus kaustophilus PolC in a ternary complex with DNA and dGTP. The structure reveals nascent base pair interactions that lead to highly… (More)
are relatively prime positive integers. We show that if u, Cu, or 2 (u,uz, then the set of positive integers can be partitioned uniquely into two disjoint sets such that the sum of any two distinct memhers of any one set is never in U. If U,>LQ and 21 u,uz. no such partition is possible. Further related results are proved which generalize theorems of… (More)
Easy proofs are given for two theorems of O. H. Mitchell about a type of generalized Vandermonde determinant. One of these results is then used to prove that if | F(e) : F\ = n where F is a field of characteristic zero and e is a root of unity of prime order, then every set of n powers of e forms an F-basis for F(e). 1. Introduction and notation. Let a =… (More)
1. Introduction. Let F p denote the field of p elements, where p is prime. A subset H ⊂ F p is a difference set (mod p) if there is a fixed integer λ > 0 such that every element of F
Let q,p be distinct primes with p — ef + 1. A variant of the Kummer-Dedekind theorem is proved for Gaussian periods, which shows in particular that q is an e-th power (modp) if and only if the Gaussian period polynomial of degree e has e (not necessarily distinct) linear factors (modg). This is applied to give a simple criterion in terms of the parameters… (More)
A complete table of 408 formulas for cyclotomic numbers of order sixteen is presented. Each number is expressed as a linear combination of parameters of quartic, octic, and bioctic Jacobi sums. Recent applications of these formulas are discussed. 1. Introduction and Notation. Let p = 16/ + 1 be a prime with a fixed primitive root g. Define the cyclotomic… (More)