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Displaying similar documents to “Singular Hecke algebras, Markov traces, and HOMFLY-type invariants”

A note on the Hermite–Rankin constant

Kazuomi Sawatani, Takao Watanabe, Kenji Okuda (2010)

Journal de Théorie des Nombres de Bordeaux

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We generalize Poor and Yuen’s inequality to the Hermite–Rankin constant γ n , k and the Bergé–Martinet constant γ n , k . Moreover, we determine explicit values of some low- dimensional Hermite–Rankin and Bergé–Martinet constants by applying Rankin’s inequality and some inequalities proven by Bergé and Martinet to explicit values of γ 5 , γ 7 , γ 4 , 2 and γ n ( n 8 ).

A generalization of Voronoï’s Theorem to algebraic lattices

Kenji Okuda, Syouji Yano (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let K be an algebraic number field and 𝒪 K the ring of integers of K . In this paper, we prove an analogue of Voronoï’s theorem for 𝒪 K -lattices and the finiteness of the number of similar isometry classes of perfect 𝒪 K -lattices.