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Displaying similar documents to “On the Frobenius number of a modular Diophantine inequality”

Numerical semigroups with a monotonic Apéry set

José Carlos Rosales, Pedro A. García-Sánchez, Juan Ignacio García-García, M. B. Branco (2005)

Czechoslovak Mathematical Journal

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We study numerical semigroups S with the property that if m is the multiplicity of S and w ( i ) is the least element of S congruent with i modulo m , then 0 < w ( 1 ) < < w ( m - 1 ) . The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.

Modular equations for some η-products

(2013)

Acta Arithmetica

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The classical modular equations involve bivariate polynomials that can be seen to be univariate in the modular invariant j with integer coefficients. Kiepert found modular equations relating some η-quotients and the Weber functions γ₂ and γ₃. In the present work, we extend this idea to double η-quotients and characterize all the parameters leading to this kind of equation. We give some properties of these equations, explain how to compute them and give numerical examples.