Sums involving the greatest integer function and Riemann-Stieltjes integration.

Berndt, Bruce C.; Dieter, Ulrich

doi:10.1515/crll.1982.337.208

Cited by 4 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where [𝑦] denotes the largest integer ≤ 𝑦 (Apostol, 1976;Berndt & Dieter, 1982). In the 19th century, Richard Dedekind made significant contributions to the fields of number theory and algebra.…”

Section: Introductionmentioning

confidence: 99%

“…Many mathematicians investigated two and three term polynomial relations by reason of they are connected to the 𝑠(𝜇, 𝛽) sums, the 𝑆(𝜇, 𝛽) sums, and several othher special finite sums (Berndt & Dieter, 1982;Pettet & Sitaramachandrarao, 1987;Simşek, 1998). Cetin et al (2014) defined new polynomials with the help of the n variable Carlitz polynomial.…”

Section: Introductionmentioning

confidence: 99%

“…(21) is given by Berndt and Dieter (1982). Cetin et al (2014) introduced the sum 𝐶(𝜇, 𝛽; 1) with the equation below:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Identities for a Special Finite Sum Related to the Dedekind Sums and Fibonacci Numbers

Çetin

2023

Gazi University Journal of Science Part A: Engineering and Innovation

View full text Add to dashboard Cite

The origin of this article is to achieve original equations related to the special finite sum C(μ,β;1), which is connected with Dedekind, Hardy, Simsek, and many other finite sums. By using the analytic properties of this sum, many useful identities are established between the C(μ,β;1) sum and other well-known finite sums. Through the use of these identities, the reciprocity law of this sum is obtained. Furthermore, another reciprocity law of the sum C(μ,β;1) is presented for μ and β are particular Fibonacci numbers. This remarkable result establishes a connection between number theory and analysis.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Identities for a Special Finite Sum Related to the Dedekind Sums and Fibonacci Numbers

Çetin

2023

Gazi University Journal of Science Part A: Engineering and Innovation

View full text Add to dashboard Cite

show abstract

Computing the Continuous Discretely

Beck

Robins

2015

Undergraduate Texts in Mathematics

288

344

View full text Add to dashboard Cite

A note on hardy type sums and Dedekind sums

Çetin

2016

Filomat

View full text Add to dashboard Cite

In [9], Cetin et al. defined a new special finite sum which is denoted by C1(h,k). In this paper, with the help of two-term polynomial relation, we will give the explicit values of the sum C1(h,k). We will see that for the odd values of h and k, this sum only depends on one variable. After that we will give many properties of this sum and connections with other well-known finite sums such as the Dedekind sums, the Hardy sums and the Simsek sums Y(h,k). By using the Fibonacci numbers and two-term polynomial relation, we will also give some relations for these sums.

show abstract

Sums involving the greatest integer function and Riemann-Stieltjes integration.

Cited by 4 publications

References 11 publications

Identities for a Special Finite Sum Related to the Dedekind Sums and Fibonacci Numbers

Identities for a Special Finite Sum Related to the Dedekind Sums and Fibonacci Numbers

Computing the Continuous Discretely

A note on hardy type sums and Dedekind sums

Contact Info

Product

Resources

About