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Application of Eichler's reduction formula to the representation of numbers by certain quaternary quadratic forms

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Abstract

It is shown how Eichler's formula can be used to obtain exact formulas for the number of representations of positive integers by certain positive-definite quadratic forms of principal type in four variables, in terms of traces of Frobenius endomorphisms of appropriate elliptic curves over fields of finite characteristic; as examples, some new exact formulas are derived.

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Authors and Affiliations

  1. Leningrad Division, V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR

    O. M. Fomenko

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  1. O. M. Fomenko
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Translated from Matematicheskie Zametki, Vol. 9, No. 1, pp. 71–76, January, 1971.

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Fomenko, O.M. Application of Eichler's reduction formula to the representation of numbers by certain quaternary quadratic forms. Mathematical Notes of the Academy of Sciences of the USSR 9, 41–44 (1971). https://doi.org/10.1007/BF01405050

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  • DOI: https://doi.org/10.1007/BF01405050

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