Lattice Reduction Over Imaginary Quadratic Fields
نویسندگان
چکیده
منابع مشابه
Explicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields by Integer Lattice Reduction*
Motivated by a constructive realization of generalized dihedral groups as Galois groups over Q and by Atkin’s primality test, we present an explicit construction of the Hilbert class fields (ring class fields) of imaginary quadratic fields (orders). This is done by first evaluating the singular moduli of level one for an imaginary quadratic order, and then constructing the “genuine” (i.e., leve...
متن کاملNormal Bases of Ray Class Fields over Imaginary Quadratic Fields
We first develop a criterion to determine normal bases (Theorem 2.4), and by making use of necessary lemmas which were refined from [3] we further prove that singular values of certain Siegel functions form normal bases of ray class fields over all imaginary quadratic fields other than Q( √−1) and Q( √−3) (Theorem 4.5 and Remark 4.6). This result would be an answer for the Lang-Schertz conjectu...
متن کاملTheta functions of quadratic forms over imaginary quadratic fields
is a modular form of weight n/2 on Γ0(N), where N is the level of Q, i.e. NQ−1 is integral and NQ−1 has even diagonal entries. This was proved by Schoeneberg [5] for even n and by Pfetzer [3] for odd n. Shimura [6] uses the Poisson summation formula to generalize their results for arbitrary n and he also computes the theta multiplier explicitly. Stark [8] gives a different proof by converting θ...
متن کاملVisualizing imaginary quadratic fields
Imaginary quadratic fields Q( √ −d), for integers d > 0, are perhaps the simplest number fields afterQ. They are equal parts helpful first example and misleading special case. LikeZ, the Gaussian integersZ[i] (the cased = 1) have unique factorization and a Euclidean algorithm. As d grows, however, these properties eventually fail, first the latter and then the former. The classical Euclidean al...
متن کامل`-adic Representations Associated to Modular Forms over Imaginary Quadratic Fields
Let π be a regular algebraic cuspidal automorphic representation of GL2 over an imaginary quadratic number field K, and let ` be a prime number. Assuming the central character of π is invariant under the non-trivial automorphism of K, it is shown that there is a continuous irreducible `-adic representation ρ of Gal(K/K) such that L(s, ρv) = L(s, πv) whenever v is a prime of K outside an explici...
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: IEEE Transactions on Signal Processing
سال: 2020
ISSN: 1053-587X,1941-0476
DOI: 10.1109/tsp.2020.3036647