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• W3107050570 abstract "In this paper, we find a basis for the space of modular forms of weight 2 on (Gamma _1(48)) and then use this basis to find formulas for the number of representations of a positive integer n by certain quaternary quadratic forms which are of the form (sum _{i=1}^4 a_i x_i^2), (sum _{i=1}^2 b_i(x_{2i-1}^2 + x_{2i-1}x_{2i}+x_{2i}^2)) and (a_1x_1^2 + a_2 x_2^2 + b_1(x_3^2+x_3x_4+x_4^2)), where (a_i)’s belong to ({1,2,3,4,6,12}) and (b_i)’s belong to ({1,2,4,8,16}). In [1], A. Alaca et al. considered similar problem for the quaternary forms (which are diagonal) with coefficients 1, 2, 3, 6. Thus, our work extends their results with additional coefficients 4 and 12, and further in our work, we consider two more types of quaternary quadratic forms which are not diagonal. Moreover, our formulas for the diagonal quaternary quadratic forms with coefficients in ({1,2,3,4,6,12}) include explicit formulas for the number of representations (of a natural number) by 8 of the Ramanujan’s universal quaternary quadratic forms [19]. We also determine some of the universal quadratic forms in the other two types of forms considered in our work." @default.
• W3107050570 created "2020-12-07" @default.
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• W3107050570 date "2020-01-01" @default.
• W3107050570 modified "2023-09-27" @default.
• W3107050570 title "On the Number of Representations of a Natural Number by Certain Quaternary Quadratic Forms" @default.
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• W3107050570 doi "https://doi.org/10.1007/978-981-15-8719-1_12" @default.
• W3107050570 hasPublicationYear "2020" @default.
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