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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1979 Volume 108(150), Number 4, Pages 567–580 (Mi sm2341)

This article is cited in 20 papers

Deficient divisors in the Valiron sense

A. S. Sadullaev


Abstract: In this article the author proves that for any holomorphic mapping $f\colon\mathbf C^n\to\mathbf P^m$ the set
$$ E_V(f)=\biggl\{A\colon\varliminf_{r\to\infty}\frac{N_f(r,A)}{T_f(r)}<1\biggr\} $$
of hyperplanes deficient in the Valiron sense forms a polar set. This gives a positive answer to a question posed by Griffiths and King.
Bibliography: 16 titles.

UDC: 517.55+517.947.42

MSC: Primary 32H30; Secondary 31C10

Received: 16.10.1978


 English version:
Mathematics of the USSR-Sbornik, 1980, 36:4, 535–547

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© Steklov Math. Inst. of RAS, 2024