منابع مشابه
The Euler Series of Restricted Chow Varieties
We are interested in understanding the geometry and topology of Chow varieties and the space of all effective cycles with the same homology class, “restricted Chow variety”. In this paper we discuss the case of projective algebraic varieties on which an algebraic torus acts linearly such that there are finitely many irreducible invariant subvarieties. The projective toric varieties are importan...
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We attach a certain n × n matrix An to the Dirichlet series L(s) = ∑ ∞ k=1 akk . We study the determinant, characteristic polynomial, eigenvalues, and eigenvectors of these matrices. The determinant of An can be understood as a weighted sum of the first n coefficients of the Dirichlet series L(s). We give an interpretation of the partial sum of a Dirichlet series as a product of eigenvalues. In...
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A method for analysing a class of divergent series is developed from the Euler– Maclaurin summation formula. The conditions that the summand must satisfy are explored, and a significant simplification is obtained for cases where the summation ranges over all integers. As an example, we consider the Ewald representation for Schlömilch series, and show that this includes Twersky’s dual series for...
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Given a projective algebraic variety X, let p(X) denote the monoid of eeective algebraic equivalence classes of eeective algebraic cycles on X. The p-th Euler-Chow series of X is an element in the formal monoid-ring Z p(X)] ] deened in terms of Euler characteristics of the Chow varieties Cp;; (X) of X, with 2 p(X). We provide a systematic treatment of such series, and give projective bundle for...
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Leonhard Euler is one of the greatest and most astounding icons in the history of science. His work, dating back to the early eighteenth century, is still with us, very much alive and generating intense interest. Like Shakespeare and Mozart, he has remained fresh and captivating because of his personality as well as his ideas and achievements in mathematics. The reasons for this phenomenon lie ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2001
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00630-0