- Dissertation: The uniqueness problem for L-functions and holomorphic curves.
- Speciality: Mathematical Analysis Code: 9460102.
- Ph. D. Candidate: Phommavong Chanthaphone.
- Supervisors:
1. Dr. Vu Hoai An.
2. Assoc. Prof. Ha Tran Phuong.
Training institution: University of Education - Thai Nguyen University.
NEW SCIENTIFIC FINDINGS OF THE DISSERTATION
1. Establish two forms of uniqueness theorems for L-functions and meromorphic functions based on algebraic conditions related to the deficiency value at infinity (Theorem 1.2.1) and algebraic conditions related to the derivatives of meromorphic functions (Theorem 1.3.1).
2. Construct two algebraic conditions for two linearly non-degenerate holomorphic curves of level 1 that share two hypersurfaces (Theorem 2.2.3) or share one hypersurface (Theorem 2.2.4) must be identical. From this, we show the existence of uniqueness hypersurfaces for the class of linearly non-degenerate holomorphic curves of level 1.
3. Based on the proof of the Second Fundamental Theorem (Theorem 3.2.1), establish a new uniqueness theorem for holomorphic curves on an annulus, with the aim hypersurfaces in subgeneral position (Theorem 3.2.2), using algebraic conditions related to the multiplicities of zeros.
APPLICATIONS IN PRACTICE AND THE NEEDS FOR FURTHER STUDIES
- Study some new forms of uniqueness theorems for meromorphic functions under algebraic conditions related to the deficiency values at the poles.
- Continue study forms of the Second Fundamental Theorem with truncated or reduced multiplicities, and apply these results to the study of uniqueness problems for holomorphic curves.
