On the cardinality of unique range sets with weight one

B. Chakraborty; S. Chakraborty

doi:10.37863/umzh.v72i7.6022

B. Chakraborty Ramakrishna Mission Vivekananda Centenary College, West Bengal, India https://orcid.org/0000-0002-3951-4792
S. Chakraborty Jadavpur Univ., West Bengal, India

DOI: https://doi.org/10.37863/umzh.v72i7.6022

Анотація

UDC 517.9

Про потужнiсть унiкального набору множин з одиничною вагою

Двi мероморфнi функцiї $f$ i $g$ сумiсно мають множину $S\subset \mathbb{C}\cup\{\infty\}$ з одиничною вагою $l\in\mathbb{N}\cup\{0\}\cup\{\infty\},$ якщо $E_{f}(S,l)=E_{g}(S,l),$ де
$$E_{f}(S,l)=\bigcup_{a \in S} \big \{(z,t) \in \mathbb{C}\times\mathbb{N} \bigm| f(z)=a \; \text{з кратністю} \;p \big \},$$ за умови, що $t=p$, якщо $p\leq l$, i $t=p+1$, якщо $p>l.$
У цiй роботi ми вдосконалюємо та доповнюємо результат L. W. Liao і C. C. Yang [Indian J. Pure and Appl. Math., 31, No~4, 431–440 (2000)], пропонуючи доведення того, що iснує скiнченна множина $S,$ що складається з 13 елементiв, така, що з $E_{f}(S,1)=E_{g}(S,1)$ випливає $f\equiv g.$

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