A sharp form of Nevanlinna's Second Main Theorem of several complex variables (Q1906896)

Recently, motivated by relations between Nevanlinna theory and the theory of heights in number theory, one has started finding precise error terms of the Second Main Theorem in Nevanlinna theory. In this paper, we first extend the best logarithmic derivative lemma from one complex variable to several complex variables. Then we prove a sharp form of the Second Main Theorem for meromorphic functions of several complex variables by using the logarithmic derivative lemma. Moreover, we obtain the best upper bound of error terms of the Second Main Theorem for meromorphic functions of finite order. Finally, we show a sharp estimate on upper bound of Nevanlinna secondary deficiency.