Determining universality of m-gonal forms with first five coefficients

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2024年7月22日

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Dayoon Park

摘要

We classify the $(a_1,a_2,a_3,a_4,a_5)$ $(a_{1}, a_{2}, a_{3}, a_{4}, a_{5})$ for which the universality of an m-gonal form $F_m({\textbf{x}})$ $F_{m} (x)$ whose first five coefficients are $(a_1,a_2,a_3,a_4,a_5)$ $(a_{1}, a_{2}, a_{3}, a_{4}, a_{5})$ is characterized as the representabilitiy of positive integers up to $m-4$ $m - 4$ and discuss some applications.