Geodesic
Singular Functions in the Problem of the Weighted Number of Integer Points on Multidimensional Hyperboloids of Special Form
Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 278-293

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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.
Keywords: circle method, weighted number of integer points, multidimensional hyperboloid, singular series, singular integral, Ramanujan sum.
Mots-clés : double Gauss sum 
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     author = {U. M. Pachev and R. A. Dokhov},
     title = {Singular {Functions} in the {Problem} of the {Weighted} {Number} of {Integer} {Points} on {Multidimensional} {Hyperboloids} of {Special} {Form}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {278--293},
     publisher = {mathdoc},
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     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a8/}
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U. M. Pachev; R. A. Dokhov. Singular Functions in the Problem of the Weighted Number of Integer Points on Multidimensional Hyperboloids of Special Form. Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 278-293. http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a8/