ENTIRE FUNCTION OF UNBOUNDED INDEX IN ANY REAL DIRECTION - Бандура, Андрій Іванович (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2019)
We prove that an entire function F( z_1 , z_2 ) = z_1 z_2 is of unbounded index in any complex direction b = (b 1 , b 2 ) ∈ C2 0. But F ( z 1 0 + b 1t , z2 0 + t ) is of bounded index for every given z 1 0 , z 2 0 as function of variable t. It is a generalization of our previous result for direction (1,1).