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The asymptotic formula in Waring’s problem
 Internat. Math. Res. Notices
"... Abstract. We derive a new minor arc bound, suitable for applications associated with Waring’s problem, from Vinogradov’s mean value theorem. In this way, the conjectured asymptotic formula in Waring’s problem is established for sums of s kth powers of natural numbers when k> 6 and s> 2k2 − 11. ..."
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Cited by 13 (12 self)
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Abstract. We derive a new minor arc bound, suitable for applications associated with Waring’s problem, from Vinogradov’s mean value theorem. In this way, the conjectured asymptotic formula in Waring’s problem is established for sums of s kth powers of natural numbers when k> 6 and s> 2k2 − 11
Asymptotic Formulae of Multivariate Bernstein Approximation
"... We expand multivariate Bernstein approximation asymptotically in this paper. Our results generalize Bernstein's asymptotic formulae in [1] (see also [5]) to the multivariate setting. AMS(MOS) Subject Classifications: 41A10, 41A60, 41A63 Key Words and phrases: Bernstein polynomials, asymptotic e ..."
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Cited by 3 (0 self)
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We expand multivariate Bernstein approximation asymptotically in this paper. Our results generalize Bernstein's asymptotic formulae in [1] (see also [5]) to the multivariate setting. AMS(MOS) Subject Classifications: 41A10, 41A60, 41A63 Key Words and phrases: Bernstein polynomials, asymptotic
Asymptotic formulas for stacks and unimodal sequences
 J. Comb. Theory, Ser. A
, 2014
"... Abstract. We study enumeration functions for unimodal sequences of positive integers, where the size of a sequence is the sum of its terms. We survey known results for a number of natural variants of unimodal sequences, including Auluck's generalized Ferrers diagrams, Wright's stacks, and ..."
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Cited by 1 (0 self)
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, and Andrews ' convex compositions. These results describe combinatorial properties, generating functions, and asymptotic formulas for the enumeration functions. We also prove several new asymptotic results that ll in the notable missing cases from the literature, including an open problem in statistical
Asymptotic Formulas and Generalized Dedekind Sums
, 1998
"... this paper describes a way to repair these errors. More generally, let f(x) = ..."
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Cited by 17 (2 self)
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this paper describes a way to repair these errors. More generally, let f(x) =
Asymptotic formulas for curve operators in TQFT
, 2014
"... Topological quantum field theories with gauge group SU2 associate to each surface with marked points Σ and each integer r> 0, vector spaces Vr(Σ) and to each simple closed curve γ in Σ Hermitian operators T γr on the spaces Vr(Σ). We show that the matrix elements of the operators T γr have an asy ..."
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an asymptotic developpement in orders of 1 r, and give a formula to compute the first two terms in terms of trace functions, generalizing results of [MP]. This property, proved in [MP] for the punctured torus and the 4holed sphere, was used by them to show that curve operators on these surfaces are Toeplitz
Asymptotic formulae for the lattice point enumerator
 CAN. JOUR. MATH
, 1999
"... Let M be a convex body such that the boundary has positive curvature. Then by a well developed theory dating back to Landau and Hlawka for large the number of lattice points in M is given by G(M) = V (M) + O( d\Gamma1\Gamma"(d)) for some positive "(d). Here we give for general con ..."
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Cited by 4 (3 self)
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Let M be a convex body such that the boundary has positive curvature. Then by a well developed theory dating back to Landau and Hlawka for large the number of lattice points in M is given by G(M) = V (M) + O( d\Gamma1\Gamma"(d)) for some positive "(d). Here we give for general convex bodies the weaker estimate jG(M) \Gamma V (M)j
Asymptotic formulas for generalized elliptictype integrals
 Comput. Math. Appl
, 1996
"... EpsteinHubbell [6] elliptictype integrals occur in radiation field problems. The object of the present paper is to consider a unified form of different elliptictype integrals, defined and developed recently by several authors. We obtain asymptotic formulas for the generalized elliptictype integr ..."
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Cited by 5 (2 self)
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EpsteinHubbell [6] elliptictype integrals occur in radiation field problems. The object of the present paper is to consider a unified form of different elliptictype integrals, defined and developed recently by several authors. We obtain asymptotic formulas for the generalized elliptic
Some asymptotic formulas on generalized . . . I
 STUDIES IN PURE MATHEMATICS, TO THE MEMORY OF PAUL TURCIN
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Results 11  20
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236,533