Geodesic
Two Results Concerning the Zeros of Functions with Finite Dirichlet Integral
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 312-316

Voir la notice de l'article provenant de la source Cambridge University Press

A function f, analytic in the unit disk, is said to have finite Dirichlet integral if 1 Geometrically, this is equivalent to f mapping the disk onto a Riemann surface of finite area. The class of Dirichlet integrable functions will be denoted by . The condition above can be restated in terms of Taylor coefficients; if f(z) = Σanzn , then if and only if Σn|an| 2 < ∞. Thus, is contained in the Hardy class H 2.In particular, every such function has boundary values almost everywhere and log |f(eiθ)| ∊ L 1(dθ).The zeros zn of a function must satisfy the Blaschke condition and f(s) = B(z)F(z), where F(z) has no zeros and is the Blaschke product with zeros zn ; see (5). 
Caughran, James G. Two Results Concerning the Zeros of Functions with Finite Dirichlet Integral. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 312-316. doi: 10.4153/CJM-1969-033-5
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