On a conjecture about class numbers of totally positive quadratic forms in totally real algebraic number fields
نویسندگان
چکیده
منابع مشابه
Perfect Forms over Totally Real Number Fields
A rational positive-definite quadratic form is perfect if it can be reconstructed from the knowledge of its minimal nonzero value m and the finite set of integral vectors v such that f(v) = m. This concept was introduced by Voronöı and later generalized by Koecher to arbitrary number fields. One knows that up to a natural “change of variables” equivalence, there are only finitely many perfect f...
متن کاملOn Shintani’s ray class invariant for totally real number fields
We introduce a ray class invariant X(C) for a totally real field, following Shintani’s work in the real quadratic case. We prove a factorization formula X(C) = X1(C) · · ·Xn(C) where each Xi(C) corresponds to a real place (Theorem 3.5). Although this factorization depends a priori on some choices (especially on a cone decomposition), we can show that it is actually independent of these choices ...
متن کاملQuadratic extensions of totally real quintic fields
In this work, we establish lists for each signature of tenth degree number fields containing a totally real quintic subfield and of discriminant less than 1013 in absolute value. For each field in the list we give its discriminant, the discriminant of its subfield, a relative polynomial generating the field over one of its subfields, the corresponding polynomial over Q, and the Galois group of ...
متن کاملClass number in totally imaginary extensions of totally real function fields
We show that, up to isomorphism, there are only finitely many totally real function fields which have any totally imaginary extension of a given ideal class number.
متن کاملCompanion Forms Over Totally Real Fields, II
We prove a companion forms theorem for mod l Hilbert modular forms. This work generalises results of Gross and Coleman–Voloch for modular forms over Q, and gives a new proof of their results in many cases.
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: 1979
ISSN: 0022-314X
DOI: 10.1016/0022-314x(79)90038-6