Genus of an entire function

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)