An explicit formula for the Hilbert symbol of a formal group

Floric Tavares Ribeiro

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The algebraic groups leading to the Roth inequalities

Masami Fujimori (2012)

Journal de Théorie des Nombres de Bordeaux

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We determine the algebraic groups which have a close relation to the inequalities.

Binary Moore-Penrose inverses of set inclusion incidence matrices.

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Séminaire Lotharingien de Combinatoire [electronic only]

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Anticyclotomic Iwasawa theory of CM elliptic curves

Adebisi Agboola, Benjamin Howard (2006)

Annales de l’institut Fourier

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We study the Iwasawa theory of a CM elliptic curve $E$ in the anticyclotomic $Z_{p}$ -extension of the CM field, where $p$ is a prime of good, ordinary reduction for $E$ . When the complex $L$ -function of $E$ vanishes to even order, Rubin’s proof of the two variable main conjecture of Iwasawa theory implies that the Pontryagin dual of the $p$ -power Selmer group over the anticyclotomic extension is a torsion Iwasawa module. When the order of vanishing is odd, work of Greenberg show that it is not a torsion...

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The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let $A, B$ denote generic binary forms, and let $𝔲_{r} = {(A, B)}_{r}$ denote their $r$ -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the ${𝔲_{r}}$ . As a consequence, we show that each of the higher transvectants ${𝔲_{r} : r \geq 2}$ is redundant in the sense that it can be completely recovered from $𝔲_{0}$ and $𝔲_{1}$ . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of $S L_{2}$ -representations,...