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Displaying similar documents to “On q -summation and confluence”

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 ≥ 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,...

A new lower bound for ∥ ( 3 / 2 ) k ∥

Wadim Zudilin (2007)

Journal de Théorie des Nombres de Bordeaux

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We prove that, for all integers k exceeding some effectively computable number  K , the distance from ( 3 / 2 ) k to the nearest integer is greater than 0 . 5803 k .