The second main theorem for small functions and related problems

From MaRDI portal

Publication:1778073

Jump to:navigation, search

DOI10.1007/BF02392741zbMath1203.30035MaRDI QIDQ1778073

Katsutoshi Yamanoi

Publication date: 27 May 2005

Published in: Acta Mathematica (Search for Journal in Brave)

Mathematics Subject Classification ID

Rational points (14G05) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.) (11J97) Global ground fields in algebraic geometry (14G25)

Related Items

Second main theorems for meromorphic mappings intersecting moving hyperplanes with truncated counting functions and unicity problem ⋮ On the uniqueness of certain type of differential-difference polynomials sharing a polynomial ⋮ ON PARTIAL VALUE SHARING RESULTS OF MEROMORPHIC FUNCTIONS WITH THEIR SHIFTS AND ITS APPLICATIONS ⋮ Uniqueness of difference-differential polynomials of meromorphic functions sharing a small function \(\mathrm{IM}\) ⋮ Defective functions of meromorphic functions in the unit disc ⋮ Uniqueness of meromorphic functions sharing values with their shifts ⋮ Topics on meromorphic mappings and defects ⋮ The concepts of general position and a second main theorem for non-linear divisors ⋮ On meromorphic functions that share three values of finite weights ⋮ Two meromorphic functions on annuli sharing some pairs of small functions or values ⋮ UNICITY OF MEROMORPHIC FUNCTIONS SHARING SOME SMALL FUNCTIONS REGARDLESS OF MULTIPLICITIES ⋮ Some further \(q\)-shift difference results on Hayman conjecture ⋮ On postsingularly finite exponential maps ⋮ Unnamed Item ⋮ On a result of Zhang and Xu concerning their open problem ⋮ Some further difference results on Hayman conjecture and value-sharing ⋮ Meromorphic functions that share values with their shifts or their \(n\)-th order differences ⋮ Two meromorphic functions share some pairs of small functions ⋮ Squarefree doubly primitive divisors in dynamical sequences ⋮ \(ABC\) implies a Zsigmondy principle for ramification ⋮ Finiteness problem of meromorphic functions sharing four small functions regardless of multiplicities ⋮ Differentiating relatively ⋮ On the uniqueness of two different classes of meromorphic functions under the sharing of two sets of rational functions ⋮ P-adic Nevanlinna theory outside of a hole ⋮ Meromorphic functions that share four or three small functions with their difference operators ⋮ Certain non-linear differential polynomials sharing a non zero polynomial ⋮ Unnamed Item ⋮ An ultrametric Nevanlinna's second main theorem for small functions of a special type ⋮ Existence of meromorphic solutions of first-order difference equations ⋮ Some results on the value distribution of differential polynomials ⋮ Uniqueness of a meromorphic function partially and normally sharing small functions with its different variants of generalized operator ⋮ Uniqueness of meromorphic functions sharing small functions dealing with multiple values in one angular domain of the unit disc ⋮ On the uniqueness of certain type of shift polynomial sharing a small function ⋮ Unnamed Item ⋮ Meromorphic functions on annuli sharing finite sets with truncated multiplicity ⋮ A precise inequality of differential polynomials related to small functions ⋮ Value sharing of non linear differential polynomials with the glimpse of normal family ⋮ A note on properties of solutions of Riccati and hyper‐Riccati equations ⋮ A note on partial sharing of values of meromorphic functions with their shifts ⋮ A SECTORIAL THEOREM ON COMPLETELY RAMIFIED RATIONAL FUNCTIONS ⋮ Portraits of preperiodic points for rational maps ⋮ On meromorphic solutions of Malmquist type difference equations ⋮ Isotriviality, integral points, and primitive primes in orbits in characteristic \(p\) ⋮ Quasiperiodicity of transcendental meromorphic functions ⋮ Meromorphic functions sharing values partially with their derivatives and shifts ⋮ Unnamed Item ⋮ Uniqueness of meromorphic functions concerning value sharing of nonlinear differential monomials ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Second main theorems for meromorphic mappings and moving hyperplanes with truncated counting functions ⋮ On a conjecture of Y. H. Cao and X. B. Zhang ⋮ On the Uniqueness of Certain Type of Difference Polynomial Sharing a Small Function ⋮ Class of meromorphic functions partially shared values with their differences or shifts ⋮ Finite index theorems for iterated Galois groups of unicritical polynomials ⋮ Unnamed Item ⋮ Nevanlinna theory and Diophantine approximation ⋮ On a certain nonlinear differential monomial sharing a nonzero polynomial ⋮ Finite index theorems for iterated Galois groups of cubic polynomials ⋮ On certain non-linear differential polynomial sharing a non-zero polynomial ⋮ Transcendental Meromorphic Solutions of P 34 and Small Targets ⋮ On the Fermat-type equation \({f^3(z)+f^3(z+c)=1}\) ⋮ On the uniqueness of certain types of differential-difference polynomials ⋮ Meromorphic functions sharing four small functions ⋮ Results on uniqueness problem for meromorphic mappings sharing moving hyperplanes in general position under more general and weak conditions ⋮ TWO MEROMORPHIC FUNCTIONS SHARING SOME PAIRS OF SMALL FUNCTIONS REGARDLESS OF MULTIPLICITIES ⋮ New results on applications of Nevanlinna methods to value sharing problems ⋮ Uniqueness of meromorphic functions sharing a small function and its applications ⋮ Further investigation "On an open problem of Zhang and Xu" ⋮ Classical 𝑝-adic Nevanlinna theory and Nevalinna Theory out of a hole ⋮ Existence of finite-order meromorphic solutions as a detector of integrability in difference equations ⋮ Derivatives of meromorphic functions sharing four small functions ⋮ On the distribution of meromorphic functions of positive hyper-order ⋮ On the equation \(f^n(z) + g^n(z) = E^{ \alpha z+ \beta }\) ⋮ Unnamed Item ⋮ Non-linear differential polynomials sharing small function with finite weight ⋮ A short note on a pair of meromorphic functions in a \(p\)-adic field, sharing a few small ones ⋮ On uniqueness of meromorphic functions partially sharing values with their \(q\)-shifts ⋮ ON THE TRUNCATED SMALL FUNCTION THEOREM IN NEVANLINNA THEORY ⋮ On the Fermat-type difference equation \(f^3(z)+[c_1f(z+c)+c_0f(z)^3=E^{\alpha z+\beta}\)] ⋮ Second main theorems with weighted counting functions and algebraic dependence of meromorphic mappings ⋮ Normal families of meromorphic functions with multiple values ⋮ Uniqueness of meromorphic functions whose derivatives share four small functions ⋮ A note on the uniqueness of certain types of differential-difference polynomials ⋮ Logarithmic difference lemma in several complex variables and partial difference equations ⋮ Meromorphic functions on annuli sharing few small functions with truncated multiplicities ⋮ New applications of the \(p\)-adic Nevanlinna theory ⋮ Meromorphic solutions of difference Riccati equations ⋮ Unnamed Item ⋮ Uniqueness of some differential-difference polynomials of entire functions sharing small function ⋮ The exceptional set in Vojta’s conjecture for algebraic points of bounded degree ⋮ Weakly weighted sharing and uniqueness of meromorphic functions ⋮ Uniqueness Results of Meromorphic Functions Concerning Small Functions ⋮ Failure of the Brauer-Manin principle for a simply connected fourfold over a global function field, via orbifold Mordell

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1778073&oldid=14126630"