Singular Functions in the Problem of the Weighted Number of Integer Points on Multidimensional Hyperboloids of Special Form
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The paper is devoted to the application of the circle method to the problem of an asymptotics of the weighted number of integer points on multidimensional hyperboloids of a special form. We prove the convergence and positivity of the singular series and obtain an asymptotic formula for the singular integral of this problem. Earlier, only estimates for the singular integral were known.
Keywordscircle method weighted number of integer points multidimensional hyperboloid double Gauss sum singular series singular integral Ramanujan sum
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