On a product related to the cubic Gauss sum, II
نویسندگان
چکیده
منابع مشابه
Higher composition laws II : On cubic analogues of Gauss composition
In our first article [2] we developed a new view of Gauss composition of binary quadratic forms which led to several new laws of composition on various other spaces of forms. Moreover, we showed that the groups arising from these composition laws were closely related to the class groups of orders in quadratic number fields, while the spaces underlying those composition laws were closely related...
متن کاملSome Problems Related to Sum-product Theorems
The study of sum-product phenomena and product phenomena is an emerging research direction in combinatorial number theory that has already produced several striking results. Many related problems are not yet fully understood, or are far from being resolved. In what follows we propose several questions where progress can be expected and should lead to advances in this general area. For two finit...
متن کاملOn a new type of stability of a radical cubic functional equation related to Jensen mapping
The aim of this paper is to introduce and solve the radical cubic functional equation $fleft(sqrt[3]{x^{3}+y^{3}}right)+fleft(sqrt[3]{x^{3}-y^{3}}right)=2f(x)$. We also investigate some stability and hyperstability results for the considered equation in 2-Banach spaces.
متن کاملGauss Optics and Gauss Sum on an Optical Phenomena
In the previous article (Found Phys. Lett. 16 325-341), we showed that a reciprocity of the Gauss sums is connected with the wave and particle complementary. In this article, we revise the previous investigation by considering a relation between the Gauss optics and the Gauss sum based upon the recent studies of the Weil representation for a finite group.
متن کاملThe Quadratic Gauss Sum Redux
Let p be an odd prime and ζ be a primitive p-root of unity. For any integer a prime to p, let ( p ) denote the Legendre symbol, which is 1 if a is a square mod p, and is −1 otherwise. Using Euler’s Criterion that a(p−1)/2 = ( p ) mod p, it follows that the Legendre symbol gives a homomorphism from the multiplicative group of nonzero elements Fp of Fp = Z/pZ to {±1}. Gauss’s law of quadratic rec...
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: Nagoya Mathematical Journal
سال: 1997
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000006413