Displaying similar documents to “On the 2 and the 3-connectedness of ample divisors on a surface.”

Arithmetically Gorenstein curves on arithmetically Cohen-Macaulay surfaces.

Alberto Dolcetti (2002)

Collectanea Mathematica

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Let Sigma C PN be a smooth connected arithmetically Cohen-Macaulay surface. Then there are at most finitely many complete linear systems on Sigma, not of the type |kH - K| (H hyperplane section and K canonical divisor on Sigma), containing arithmetically Gorenstein curves.

The range of the sum-of-proper-divisors function

Florian Luca, Carl Pomerance (2015)

Acta Arithmetica

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Answering a question of Erdős, we show that a positive proportion of even numbers are in the form s(n), where s(n) = σ(n) - n, the sum of proper divisors of n.

On the average of the sum-of-a-divisors function

Shi-Chao Chen, Yong-Gao Chen (2004)

Colloquium Mathematicae

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We prove an Ω result on the average of the sum of the divisors of n which are relatively coprime to any given integer a. This generalizes the earlier result for a prime proved by Adhikari, Coppola and Mukhopadhyay.

On ramifications divisors of functions in a punctured compact Riemann surface.

Pascual Cutillas Ripoll (1989)

Publicacions Matemàtiques

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Let ν be a compact Riemann surface and ν' be the complement in ν of a nonvoid finite subset. Let M(ν') be the field of meromorphic functions in ν'. In this paper we study the ramification divisors of the functions in M(ν') which have exponential singularities of finite degree at the points of ν-ν', and one proves, for instance, that if a function in M(ν') belongs to the subfield generated by the functions of this type, and has a finite ramification divisor, it also has a finite divisor....