منابع مشابه
Gröbner Bases in Orders of Algebraic Number Fields
In the 1960s Bruno Buchberger presented his first critical-pair-completion algorithm, now called Buchberger’s algorithm. Since then Gröbner bases have become a powerful tool in computational algebra and algebraic geometry. What is not as well known is that Buchberger (1985, 1987) has also shown a way of computing Gröbner bases in the integers. This is not as trivial as it may seem. In the polyn...
متن کاملWaring’s Problem for Matrices over Orders in Algebraic Number Fields
In this paper we give necessary and sufficient trace conditions for an n×n matrix over any commutative and associative ring with unity to be a sum of k-th powers of matrices over that ring, where n, k ≥ 2 are integers. We prove a discriminant criterion for every 2×2 matrix over an order R in an algebraic number field to be a sum of cubes and fourth powers of matrices over R. We also show that i...
متن کاملThe Analytic Class Number Formula for Orders in Products of Number Fields
We derive an analytic class number formula for an arbitrary order in a product of number fields.
متن کاملComputing all power integral bases in orders of totally real cyclic sextic number fields
An algorithm is given for determining all power integral bases in orders of totally real cyclic sextic number fields. The orders considered are in most cases the maximal orders of the fields. The corresponding index form equation is reduced to a relative Thue equation of degree 3 over the quadratic subfield and to some inhomogeneous Thue equations of degree 3 over the rationals. At the end of t...
متن کاملClass Numbers of Orders in Quartic Fields
as x → ∞, where L(x) is the function L(x) = ∫ x 1 e t dt. Sarnak established this result by identifying the regulators with lengths of closed geodesics of the modular curve SL2(Z)\H, where H denotes the upper half-plane, and using the Prime Geodesic Theorem for this Riemannian surface. Actually Sarnak proved not this result but the analogue where h(O) is replaced by the class number in the narr...
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: Banach Center Publications
سال: 2020
ISSN: 0137-6934,1730-6299
DOI: 10.4064/bc121-14