Number Theory and Its Applications

Li, Fuhuo; Nian-liang, Wang; Kanemitsu, Shigeru

doi:10.1142/8601

Cited by 10 publications

(19 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…73-75) of using the Ewald expansion ( [11], Chapter 5) as opposed to the Fourier-Bessel expansion alluded to above. Since it is equivalent to the Lerch functional equation ( [17], eorem 5.3, p. 130) which in turn is equivalent to an asymmetric form (3) of the functional equation for the Riemann zeta-function, we thereby show that, in the long run, the genesis is in the functional equation for the Riemann zeta-function.…”

Section: Introductionmentioning

confidence: 70%

See 1 more Smart Citation

Around the Lipschitz Summation Formula

Li¹,

Li²,

Mehta

2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Boundary behavior of important functions has been an object of intensive research since the time of Riemann. Kurokawa, Kurokawa-Koyama, and Chapman studied the boundary behavior of generalized Eisenstein series which falls into this category. The underlying principle is the use of the Lipschitz summation formula. Our purpose is to show that it is a form of the functional equation for the Lipschitz–Lerch transcendent (and in the long run, it is equivalent to that for the Riemann zeta-function) and that this being indeed a boundary function of the Hurwitz–Lerch zeta-function, one can extract essential information. We also elucidate the relation between Ramanujan’s formula and automorphy of Eisenstein series.

show abstract

Section: Introductionmentioning

confidence: 70%

“…us, we have established. Theorem 1. e Bochner modular relation (14) entails at one end of the spectrum α � − (2ϰ + 1) Ramanujan's formula (17) and at the other end α � 2ϰ + 1 the automorphy of the Eisenstein series (27), thus abridging analytic number theory and the theory of modular forms.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Around the Lipschitz Summation Formula

Li¹,

Li²,

Mehta

2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…89-109] etc. The theory of DFT for arithmetic functions has been developed in [52] in the case of periodic functions. Cf.…”

Section: Theorem 1 ([86 Theorem 3])mentioning

confidence: 99%

“…The generalized Euler constants γ k (a, M) in (52) for an arithmetic progression is naturally a highlighted subject and after [7], [46], [36], and [24], Shirasaka [69] is a culmination providing the genuine generating function for them, based on the theory of Hurwitz zeta-function. In another direction, [32] and [13] are another summit of the study on periodic Dirichlet series, appealing to the Deninger-Meyer method, based on the theory of Lerch zeta-function.…”

Section: Introductionmentioning

confidence: 99%

Limiting Values and Functional and Difference Equations

Wang¹,

Agarwal²,

Kanemitsu³

2020

Preprint

View full text Add to dashboard Cite

Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. This involves the expression for the Laurent coefficients including the residue, the Kronecker limit formulas and higher order coefficients as well as the difference formed to cancel the inaccessible part, typically the Clausen functions. We also state Abelian results which yield asymptotic formulas for weighted summatory function from that for the original summatory function.This clarifies the second equality in (62). For a general form, cf. (98).Comtet [19, pp. 224-229] is the most informative reference book on Stirling numbers.Preprints (www.preprints.org) | NOT PEER-REVIEWED |

show abstract

“…To the 1990s, this education mode has been got an impact in the education system gradually. After years of repeated practice tests, OBE model has been developing rapidly in the 21st century [1]. In recent years, the Hong Kong education funding council gradually carried out this teaching idea in institutions of higher learning reform.…”

Section: Introductionmentioning

confidence: 99%

The Comparison and Inspiration of Outcome-based Curriculum Design in Canada and Higher Vocational Education in China

Wang¹

2013

Proceedings of the 2nd International Conference on Management Science and Industrial Engineering (MSIE 2013)

View full text Add to dashboard Cite

Abstract. This paper describes the basic ideas of the Canadian outcome-based education (OBE) mode. Real-world-relevant and measurable learning outcomes are the cores of OBE. A prescribed syntactical pattern is given to describe learning outcome. Then, the development procedures for curriculum system under the OBE pattern are put forward. Compare with the Chinese curriculum system design process based on job post, this paper summarizes the inspirations to higher vocational education in China.

show abstract

Number Theory and Its Applications

Cited by 10 publications

References 0 publications

Around the Lipschitz Summation Formula

Around the Lipschitz Summation Formula

Limiting Values and Functional and Difference Equations

The Comparison and Inspiration of Outcome-based Curriculum Design in Canada and Higher Vocational Education in China

Contact Info

Product

Resources

About