منابع مشابه
A Trinity of the Borcherds Φ-function
We discuss a trinity, i.e., three distinct expressions, of the Borcherds Φ-function on the analogy of the trinity of the Dedekind η-function.
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We consider an equivariant analogue of a conjecture of Borcherds. Let (Y, σ) be a real K3 surface without real points. We shall prove that the equivariant determinant of the Laplacian of (Y, σ) with respect to a σ-invariant Ricci-flat Kähler metric is expressed as the norm of the Borcherds Φ-function at the “period point”. Here the period of (Y, σ) is not the one in algebraic geometry.
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Write Θ for the stable character associated to a finite dimensional representation E of a connected real reductive group G. Let M be the centralizer of a maximal torus T , and denote by ΦM (γ,Θ ) Arthur’s extension of |D M (γ)| 1 2Θ(γ) to T (R). In this paper we give a simple explicit expression for ΦM (γ,Θ ), when γ is elliptic in G.
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chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
15 صفحه اولDifferential Resultants and Subresultants
Consider two differential operators L1 = ∑ aid i and L2 = ∑ bjd j with coefficients in a differential field, say C(t) with d = ∂ ∂t for example. If the ai and bj are constants, the condition for the existence of a solution y of L1(y) = L2(y) = 0 is that the resultant in X of the polynomials (in C[X]) ∑ aiX i and ∑ bjX j is zero. A natural question is: how one could extend this for the case of n...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2018
ISSN: 1080-6377
DOI: 10.1353/ajm.2018.0045