LAUSR

Asymptotic expansions of the prime counting function

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1 Published in 2021 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2021.07.032

Abstract: We provide several asymptotic expansions of the prime counting function $\pi(x)$ and related functions. We define an {\it asymptotic continued fraction expansion} of a complex-valued function of a real or complex variable to be a… read more here.

Keywords: asymptotic expansions; continued fraction; prime counting; expansions prime ... See more keywords

Asymptotic expansions of density of normalized extremes from logarithmic general error distribution

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0 Published in 2017 at "Communications in Statistics - Theory and Methods"

DOI: 10.1080/03610926.2015.1062109

Abstract: ABSTRACT Logarithmic general error distribution is an extension of the log-normal distribution. In this paper, the asymptotic expansions of densities of normalized maximum from logarithmic general error distribution are derived under two different kinds of… read more here.

Keywords: asymptotic expansions; logarithmic general; general error; error distribution ... See more keywords

Asymptotic expansions for field moments of bound states

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2 Published in 2023 at "Journal of Physics A: Mathematical and Theoretical"

DOI: 10.1088/1751-8121/acd310

Abstract: Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the stable aggregate of flexible element (SAFE) method and include only the first non-zero wave-related… read more here.

Keywords: bound states; field moments; moments bound; asymptotic expansions ... See more keywords

Asymptotic expansions of the Witten–Reshetikhin–Turaev invariants of mapping tori I

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1 Published in 2018 at "Transactions of the American Mathematical Society"

DOI: 10.1090/tran/7740

Abstract: In this paper we engage in a general study of the asymptotic expansion of the Witten–Reshetikhin–Turaev invariants of mapping tori of surface mapping class group elements. We use the geometric construction of the Witten–Reshetikhin–Turaev topological… read more here.

Keywords: reshetikhin turaev; asymptotic expansions; mapping tori; turaev invariants ... See more keywords

On the asymptotic expansions of the Kashaev invariant of hyperbolic knots with seven crossings

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1 Published in 2017 at "International Journal of Mathematics"

DOI: 10.1142/s0129167x17500963

Abstract: We give presentations of the asymptotic expansions of the Kashaev invariant of hyperbolic knots with seven crossings. As the volume conjecture states, the leading terms of the expansions present the hyperbolic volume and the Chern–Simons… read more here.

Keywords: expansions kashaev; invariant hyperbolic; asymptotic expansions; kashaev invariant ... See more keywords