Abstract:Asymptotic expansions for the number of lattice points in regions of the ddimensional Euclidean space are obtained. We assume that the regions are level sets of poly
“…There are several ways to obtain it. We use the following expansion of a sufficiently smooth complex-valued function g : R s → C due to Bentkus and Götze [1]. Let J ∈ N, and x, u 1 , .…”
Section: The Hardy-littlewood Method Letmentioning
confidence: 99%
“…With this choice t lies on the boundary of M ∆(t) (1,1). Hence t ∈ m ∆(t) and the definition (10) or (9) implies, for every…”
Section: Proof Of Theorem 3 We Have To Prove That ω(F ) > D Implies mentioning
confidence: 97%
“…(1) One only has to observe that A F (R + ε) = A F (R) for R ∈ N and 0 < ε < 1, but vol(D F (R + ε)) − vol(D F (R)) R s/d−1 . Our aim is to give a sharp upper bound for P F (R).…”
Section: R) Then a F (R) Is Approximately Equal To Vol(d F (R)) It mentioning
confidence: 99%
“…Recently, Bentkus and Götze [1] studied P F (R) for polynomials F with real coefficients and leading homogeneous part…”
Section: R) Then a F (R) Is Approximately Equal To Vol(d F (R)) It mentioning
“…There are several ways to obtain it. We use the following expansion of a sufficiently smooth complex-valued function g : R s → C due to Bentkus and Götze [1]. Let J ∈ N, and x, u 1 , .…”
Section: The Hardy-littlewood Method Letmentioning
confidence: 99%
“…With this choice t lies on the boundary of M ∆(t) (1,1). Hence t ∈ m ∆(t) and the definition (10) or (9) implies, for every…”
Section: Proof Of Theorem 3 We Have To Prove That ω(F ) > D Implies mentioning
confidence: 97%
“…(1) One only has to observe that A F (R + ε) = A F (R) for R ∈ N and 0 < ε < 1, but vol(D F (R + ε)) − vol(D F (R)) R s/d−1 . Our aim is to give a sharp upper bound for P F (R).…”
Section: R) Then a F (R) Is Approximately Equal To Vol(d F (R)) It mentioning
confidence: 99%
“…Recently, Bentkus and Götze [1] studied P F (R) for polynomials F with real coefficients and leading homogeneous part…”
Section: R) Then a F (R) Is Approximately Equal To Vol(d F (R)) It mentioning
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