A reconsideration of Legendre-Jacobi symbols
نویسندگان
چکیده
منابع مشابه
Evaluation of Certain Legendre Symbols
We state and prove an apparently hitherto unrecorded evaluation of certain Legendre symbols: if p is prime, p 6= 2, and ab = p − 1, then the Legendre symbol ( b p ) is given by ( b p ) = (−1).
متن کاملSome Sums of Legendre and Jacobi Polynomials
We prove identities involving sums of Legendre and Jacobi polynomials. The identities are related to Green’s functions for powers of the invariant Laplacian and to the Minakshisundaram-Pleijel zeta function.
متن کاملSequences related to Legendre/Jacobi sequences
Two families of binary sequences are constructed from dth order cyclotomic generator and from dth order generalized cyclotomic generator with respect to two distinct primes respectively. By using estimates of certain exponential sums over rings or fields, the upper bounds of both the well-distribution measure and the order k (at least for small k) correlation measure of the resulting binary seq...
متن کاملGauss Legendre-Gauss Jacobi quadrature rules over a tetrahedral region
This paper presents a Gaussian quadrature method for the evaluation of the triple integral ( , , ) T I f x y z d xd yd z = ∫∫∫ , where ) , , ( z y x f is an analytic function in , , x y z and T refers to the standard tetrahedral region:{( , , ) 0 , , 1, 1} x y z x y z x y z ≤ ≤ + + ≤ in three space( , , ). x y z Mathematical transformation from ( , , ) x y z space to ( , , ) u v w space maps th...
متن کاملA Modified Jacobi Sequence Construction Using Multi-Rate Legendre Sequences
This paper investigates the generation of a binary Modified Jacobi sequence by means of an additive combination of constituent binary Legendre sequences which are clocked at different rates. These multi-rate combinations demonstrate that sequences of large linear complexity can be generated without resorting to linear feedback shift registers (LFSRs) of large length. Results on the linear compl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1973
ISSN: 0022-314X
DOI: 10.1016/0022-314x(73)90013-9