Recently, a paper co-authored by Professor Cao Tingbin from the Department of Mathematics of our school and Professor Zheng Jianhua from Tsinghua University, titled "Nevanlinna theory for tropical hypersurfaces," has been officially published in the internationally renowned mathematics journal Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Nanchang University is listed as the first affiliation.

This research represents a significant advancement in tropical (max-plus) value distribution theory. For the first time, it generalizes the Second Main Theorem from tropical hyperplanes to general tropical hypersurfaces, breaking a long-standing theoretical bottleneck in the field that was previously confined to tropical linear cases. The main innovations are reflected in three aspects: First, it introduces and characterizes the concept of tropically algebraically non-degenerate holomorphic curves, laying the foundation for higher-dimensional intersection theory. Second, it improves the function growth conditions by strengthening the tropical logarithmic derivative lemma, relaxing the requirement of the hyper-order being strictly less than 1 to the minimal hyper-type, thereby broadening the applicability of the theorem. Third, it proposes a more concise form of the Second Main Theorem for the one-dimensional case. The findings systematically enhance the theoretical framework of tropical value distribution and establish profound correspondences with classical complex geometry, providing powerful tools for ultradiscrete systems, tropical geometry, and related dynamical systems.

Established in 1871, Annali della Scuola Normale Superiore di Pisa - Classe di Scienze is widely recognized as one of the top-tier specialized journals in the field of mathematics. It focuses on pure mathematics and theoretical physics and is renowned for publishing major theoretical achievements and rigorous peer review. The journal publishes approximately 60 articles annually and holds significant academic influence.

Link to the paper:
https://journals.sns.it/index.php/annaliscienze/article/view/6151