[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2003.40.6.963

ON q-ANALGUE OF THE TWISTED L-FUNCTIONS AND q-TWISTED BERNOULLI NUMBERS

Simsek, Yilmaz (University of Mersin Faculty of Science Department of Mathematics)

Publication Information

Journal of the Korean Mathematical Society / v.40, no.6, 2003 , pp. 963-975 More about this Journal

Abstract

The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\;X,\;{\xi})$ is also given explicitly.

Keywords

Dirichlet L-functions; twisted L-functions; Hurwitz zeta function; generalized Bernoulli numbers and polynomials; q-analogues of the Dirichlet series and q-L-series; q-Bernoulli numbers;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)
Times Cited By Web Of Science : 10 (Related Records In Web of Science)
Times Cited By SCOPUS : 12

1	q-Analogue of Riemann's <TEX>${\varsigma}$</TEX>-function and q-Euler Numbers / [ J.Satoh ] / J. Number Theory DOI
2	A Note on q-Analogues of the Dirichlet Series and q-Bernoulli numbers / [ H.Tsumura ] / J. Number Theory DOI
3	On Carlitz's q-Bernoulli Numbers / [ N.Koblitz ] / J. Number Theory DOI
4	q-Bernoulli numbers and polynomials / [ L.Carlitz ] / Duke Math. J. DOI
5	/ [ Y.Simsek ] / Theorems on Twisted L-functions and Twisted Bernoulli numbers
6	q-Volkenborn Integration / [ T.Kim ] / Russian J. Math. Phys.
7	A New Proof of Certain formulas for p-adic L-Functions / [ N.Koblitz ] / Duke Math. J. DOI
8	Generalized Carlitz's q-Bernoulli numbers in the p-adic number fields / [ T.Kim;S.H.Rim ] / Adv. Stud. Contemp. Math.
9	P-adic Analysis: a Short Course on Recent Work / [ N.Koblitz ] / London Math. Soc. Lecture Note Ser.
10	On p-Adic q-Bernoulli Numbers / [ T.Kim ] / J. Korean Math. Soc. 과학기술학회마을
11	On a q-Analogue of the p-Adic Log Gamma functions and related Integrals / [ T.Kim ] / J. Number Theory DOI ScienceOn
12	/ [ K.Iwasawa ] / Lectures on p-adic L-Functions

1	Yilmaz Simsek. (2007) Journal of Nonlinear Mathematical Physics New approach to the complete sum of products of the twisted (h,q)-Bernoulli numbers and polynomials / 14 (1) , 44
1	Yilmaz Simsek. (2007) Applied Mathematics and Computation On twisted q-Hurwitz zeta function and q-two-variable L-function / 187 (1) , 466
12	Yilmaz Simsek. (2009) Nonlinear Analysis: Theory, Methods & Applications q-Hardy–Berndt type sums associated with q-Genocchi type zeta and q-l-functions / 71 (12) , e377
10	Yilmaz Simsek. (2010) Applied Mathematics and Computation A family of p-adic twisted interpolation functions associated with the modified Bernoulli numbers / 216 (10) , 2976
1	Yilmaz Simsek. (2006) Journal of Mathematical Analysis and Applications q-Dedekind type sums related to q-zeta function and basic L-series / 318 (1) , 333
3	Y. Simsek. (2006) Russian Journal of Mathematical Physics On p-adic twisted q-L-functions related to generalized twisted Bernoulli numbers / 13 (3) , 340
2	Yilmaz Simsek. (2006) Journal of Mathematical Analysis and Applications Twisted <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mo stretchy="false">(</mml:mo><mml:mi>h</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Bernoulli numbers and polynomials related to twisted <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mo stretchy="false">(</mml:mo><mml:mi>h</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-zeta function and L-function / 324 (2) , 790
2	H. Ozden. (2014) Acta Mathematica Hungarica Unified presentation of p-adic L-functions associated with unification of the special numbers / 144 (2) , 515
6	Yilmaz Simsek. (2010) Computers & Mathematics with Applications Twisted <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>p</mml:mi></mml:math>-adic <mml:math altimg="si2.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mrow><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-<mml:math altimg="si3.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>L</mml:mi></mml:math>-functions / 59 (6) , 2097
1	(2018) Journal of Inequalities and Applications Identities and recurrence relations of special numbers and polynomials of higher order by analysis of their generating functions / 2018 (1)

1	/ Journal of Mathematical Analysis and Applications
2	/ Journal of Mathematical Analysis and Applications
3	/ Applied Mathematics and Computation (New York)
4	/ Computers and Mathematics with Applications
5	/ Russian Journal of Mathematical Physics
6	/ Nonlinear Analysis, Theory, Methods and Applications
7	/ Journal of Nonlinear Mathematical Physics
8	/ Advanced Studies in Contemporary Mathematics (Kyungshang)
9	/ Journal of the Korean Mathematical Society
10	/ Advanced Studies in Contemporary Mathematics (Kyungshang)
11	/ Applied Mathematics and Computation (New York)
12	/ AIP Conference Proceedings

1	THE BEHAVIOR OF THE TWISTED p-ADIC (h, q)-L-FUNCTIONS AT s = 0 / [Simsek, Yilmaz;] / Journal of the Korean Mathematical Society
2	Twisted Dedekind Type Sums Associated with Barnes' Type Multiple Frobenius-Euler $l$ -Functions / [Can, Mumun;Cenkci, Mehmet;Kurt, Veli;Simsek, Yilmaz;] / Advanced Studies in Contemporary Mathematics