Webtheorem of STICKELBERGER-SCHUR on congruence relations of b(A/K)mod 4 is true in full generality (cf. 2.6). The signature of a discriminant is always defined and has the expected interpretation. Of particular interest are, as in the rational case, the quadratic discriminants. We shall give a complete Web2. Exercise #7 on page 15: The discriminant d K of an algebraic number eld K is always 0 (mod 4) or 1 (mod 4) (Stickelberger’s discriminant relation). Hint: The determinant det(˙ i! j) of an integral basis ! j is a sum of terms, each pre xed by a positive or a negative sign. Writing P, resp. N, for the sum of the positive, resp. negative ...
abstract algebra - The discriminant and Stickelberger
WebSep 1, 1984 · The occurrence of Stickelberger's relation (1.2) suggests a connection between our result and McCulloh's characterization [9] of the stable isomorphism classes … the simple plant
On the index of the Stickelberger ideal and the cyclotomic
WebApr 1, 2024 · Abstract. The worst-case hardness of finding short vectors in ideals of cyclotomic number fields (Ideal-SVP) is a central matter in lattice based cryptography. Assuming the worst-case hardness of Ideal-SVP allows to prove the Ring-LWE and Ring-SIS assumptions, and therefore to prove the security of numerous cryptographic schemes … WebIn 1897, Stickelberger published the paper [28] discussed in the Introduction. The main focus here is on properties of the discriminant D of a number field Ω. … WebThey will form the Stickelberger ideal. The proof involves factoring Gauss sums as products of prime ideals, and since Gauss sums generate principal ideals, we obtain relations in the ideal class group. As an application, we prove Herbrand’s theorem which relates the nontriviality of certain parts of the ideal class group of ℚ (ζ p ) to p ... the simple practice client portal