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Genus of an entire function

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The integer equal to the larger of the two numbers and in the representation of the entire function in the form

(*)

where is the degree of the polynomial and is the least integer satisfying the condition

The number is called the genus of the product appearing in formula (*).

References

[1] B.Ya. Levin, "Distribution of zeros of entire functions" , Amer. Math. Soc. (1964) (Translated from Russian)


Comments

The genus plays a role in factorization theorems for entire functions, cf. e.g. Hadamard theorem; Weierstrass theorem.

References

[a1] R.P. Boas, "Entire functions" , Acad. Press (1954)
How to Cite This Entry:
Genus of an entire function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Genus_of_an_entire_function&oldid=47082
This article was adapted from an original article by A.F. Leont'ev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article