Ordinary forms and their local Galois representations
... end of Gross’ paper [10]) that the mod p form associated to ∆ does not have a companion form for p < 3, 500 except p = 23 and p = 691. In the former case ∆ is its own mod p companion form (note τ (n) ≡ n11 τ (n) mod 23 for all n coprime to 23), and in the latter case ρ̄∆ is (globally) completely red ...
... end of Gross’ paper [10]) that the mod p form associated to ∆ does not have a companion form for p < 3, 500 except p = 23 and p = 691. In the former case ∆ is its own mod p companion form (note τ (n) ≡ n11 τ (n) mod 23 for all n coprime to 23), and in the latter case ρ̄∆ is (globally) completely red ...
Joining Multiple Rank-1 Lattices
... In the years after the seminal results for integration lattices [27], several papers picked up the idea of approximating functions using the sampling values along rank-1 lattices, cf. [21, 30, 18, 19, 20, 22]. The error bounds for the approximation of functions of dominating mixed smoothness are alm ...
... In the years after the seminal results for integration lattices [27], several papers picked up the idea of approximating functions using the sampling values along rank-1 lattices, cf. [21, 30, 18, 19, 20, 22]. The error bounds for the approximation of functions of dominating mixed smoothness are alm ...
Mathematics Course 111: Algebra I Part II: Groups
... Example. The set of all transformations of the plane that are of the form (x, y) 7→ (ax + by, cx + dy) with ad − bc 6= 0 is a group with respect to the operation of composition of transformations. This group includes all rotations about the origin, and all reflections in lines passing through the or ...
... Example. The set of all transformations of the plane that are of the form (x, y) 7→ (ax + by, cx + dy) with ad − bc 6= 0 is a group with respect to the operation of composition of transformations. This group includes all rotations about the origin, and all reflections in lines passing through the or ...
On the field of definition of superspecial polarized
... type number of End(A). But, when dim A 2, all the abelian varieties as above are isomorphic with each other and have a model defined over Fp (This fact is due to Shioda, Deligne and Ogus). In this case, the arithmetic of quaternion hermitian lattices is mainly reflected on the nature of polarization ...
... type number of End(A). But, when dim A 2, all the abelian varieties as above are isomorphic with each other and have a model defined over Fp (This fact is due to Shioda, Deligne and Ogus). In this case, the arithmetic of quaternion hermitian lattices is mainly reflected on the nature of polarization ...
THE DYNAMICAL MORDELL-LANG PROBLEM FOR NOETHERIAN SPACES
... a periodic subvariety. He showed, for any morphism of varieties over a field of characteristic 0, that S cannot be very dense of order 2 (see [7, Définition 2]); this is a weaker conclusion than being of Banach density 0 (which is the result of our Proposition 1.6). We also note that Denis [7, Ques ...
... a periodic subvariety. He showed, for any morphism of varieties over a field of characteristic 0, that S cannot be very dense of order 2 (see [7, Définition 2]); this is a weaker conclusion than being of Banach density 0 (which is the result of our Proposition 1.6). We also note that Denis [7, Ques ...
Physics On the Generators of Quantum Dynamical Semigroups
... system S + R which rigorously imply a semigroup law of motion for the subsystem S. Intuitively the time scale considered for S should be very long compared with the relaxation time of the external system R, but shorter than the recurrence time for the system S + R considered as a closed finite syste ...
... system S + R which rigorously imply a semigroup law of motion for the subsystem S. Intuitively the time scale considered for S should be very long compared with the relaxation time of the external system R, but shorter than the recurrence time for the system S + R considered as a closed finite syste ...
Birkhoff's representation theorem
This is about lattice theory. For other similarly named results, see Birkhoff's theorem (disambiguation).In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations correspond to unions and intersections of sets. The theorem can be interpreted as providing a one-to-one correspondence between distributive lattices and partial orders, between quasi-ordinal knowledge spaces and preorders, or between finite topological spaces and preorders. It is named after Garrett Birkhoff, who published a proof of it in 1937.The name “Birkhoff's representation theorem” has also been applied to two other results of Birkhoff, one from 1935 on the representation of Boolean algebras as families of sets closed under union, intersection, and complement (so-called fields of sets, closely related to the rings of sets used by Birkhoff to represent distributive lattices), and Birkhoff's HSP theorem representing algebras as products of irreducible algebras. Birkhoff's representation theorem has also been called the fundamental theorem for finite distributive lattices.