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Certain analogues of the Hardyh-Litlewood problem and density methods

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Abstract

Applying density methods of the theory of the Dirichlet L-functions, one finds an asymptotic formula for the number of solutions of the equations of the type N=ϕ(x,y)+m and N=m−ϕ(x,y), where ϕ(x,y) is a positive primitive quadratic form, while m is representable by a sum of two squares and runs through its values without repetition.

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Authors
  1. F. B. Koval'chik
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 121–142, 1981.

In conclusion, I express my sincere gratitude to A. I. Vinogradov for useful discussions.

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Koval'chik, F.B. Certain analogues of the Hardyh-Litlewood problem and density methods. J Math Sci 25, 1057–1072 (1984). https://doi.org/10.1007/BF01680829

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  • DOI: https://doi.org/10.1007/BF01680829

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