Determining universality of $m$ -gonal form with first five coefficients

preprint2021arXivOpen access

In this paper, we classify the $(a_1,a_2,a_3,a_4,a_5)$ for which the universality of an $m$ -gonal form $F_m(\mathbf x)$ having its first five coefficients as $(a_1,a_2,a_3,a_4,a_5)$ is characterized as the representability of positive integers up to $m-4$ and see its applications.

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Determining universality of $m$ -gonal form with first five coefficients

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Determining universality of mmm-gonal form with first five coefficients

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Determining universality of $m$ -gonal form with first five coefficients