Wachstumseigenschaften ganzer Funktionen mit negativen Nullstellen (Q792483)

Let f(z) be an entire function with order and lower order \(\rho\) and \(\lambda\) respectively. Generalizing earlier results concerning the maximum and minimum modulus on \(| z| =r\) the author compares the growth of the function in two different directions \(\theta\) and \(\phi\), supposing that all zeros are negative and \(\rho\) non-integral. If the upper and lower limits (as \(r\to \infty)\) of \(\log | f(re^{i\theta})| /\log | f(re^{i\phi})|\) are denoted A and B, a main result is that \(A\geq \cos \rho \theta /\cos \rho \phi \geq B\) when \(\phi\) is restricted to certain intervals of total length \(\pi\) (more special results if \(\rho\) or \(\lambda<1)\). The method consists of skillful use of integral equalities and inequalities.