Higher congruence companion forms
نویسندگان
چکیده
منابع مشابه
Canonical Forms for Unitary Congruence and *Congruence
We use methods of the general theory of congruence and *congruence for complex matrices—regularization and cosquares—to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices A such that ĀA (respectively, A) is normal. As special cases of our canonical forms, we obtain—in a coherent and systematic way—known canonical forms for con...
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Let F : U × · · · × U → K, G : V × · · · × V → K be two n-linear forms with n > 2 on vector spaces U and V over a field K. We say that F and G are symmetrically equivalent if there exist linear bijections φ1, . . . , φn : U → V such that F (u1, . . . , un) = G(φi1u1, . . . , φinun) for all u1, . . . , un ∈ U and each reordering i1, . . . , in of 1, . . . , n. The forms are said to be congruent ...
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We have three motivations for looking at this theorem. Firstly it can be seen as partial confirmation of a conjecture of Fontaine and Mazur which asserts that if ρ : GQ → GLn(Qp) is a continuous irreducible representation ramified at only finitely many primes and such that the image of the inertia group at p is finite, then the image of ρ is finite (see [FM]). Our theorem verifies this conjectu...
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Canonical forms for congruence and *congruence of square complex matrices were given by Horn and Sergeichuk in [Linear Algebra Appl. 389 (2004) 347–353], based on Sergeichuk’s paper [Math. USSR, Izvestiya 31 (3) (1988) 481–501], which employed the theory of representations of quivers with involution. We use standard methods of matrix analysis to prove directly that these forms are canonical. Ou...
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Let X35 be a Siegel cusp form of degree 2 and weight 35. Kikuta, Kodama and Nagaoka [4] proved that det T a(T, X35) ≡ 0 mod 23 for every half integral positive symmetric matrix T . In this paper, we give a finite number of examples of Hecke eigenforms of degree 2 and odd weights that have the same type of congruence relation above. We also introduce congruence relations for the Hecke eigenvalue...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2012
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa156-2-4