# Integral identities and constructions of approximations to zeta-values

Journal de théorie des nombres de Bordeaux (2003)

- Volume: 15, Issue: 2, page 535-550
- ISSN: 1246-7405

## Access Full Article

top## Abstract

top## How to cite

topNesterenko, Yuri V.. "Integral identities and constructions of approximations to zeta-values." Journal de théorie des nombres de Bordeaux 15.2 (2003): 535-550. <http://eudml.org/doc/249071>.

@article{Nesterenko2003,

abstract = {Some general construction of linear forms with rational coefficients in values of Riemann zeta-function at integer points is presented. These linear forms are expressed in terms of complex integrals of Barnes type that allows to estimate them. Some identity connecting these integrals and multiple integrals on the real unit cube is proved.},

author = {Nesterenko, Yuri V.},

journal = {Journal de théorie des nombres de Bordeaux},

keywords = {zeta function; linear forms in polylogarithms; hypergoemetric integrals},

language = {eng},

number = {2},

pages = {535-550},

publisher = {Université Bordeaux I},

title = {Integral identities and constructions of approximations to zeta-values},

url = {http://eudml.org/doc/249071},

volume = {15},

year = {2003},

}

TY - JOUR

AU - Nesterenko, Yuri V.

TI - Integral identities and constructions of approximations to zeta-values

JO - Journal de théorie des nombres de Bordeaux

PY - 2003

PB - Université Bordeaux I

VL - 15

IS - 2

SP - 535

EP - 550

AB - Some general construction of linear forms with rational coefficients in values of Riemann zeta-function at integer points is presented. These linear forms are expressed in terms of complex integrals of Barnes type that allows to estimate them. Some identity connecting these integrals and multiple integrals on the real unit cube is proved.

LA - eng

KW - zeta function; linear forms in polylogarithms; hypergoemetric integrals

UR - http://eudml.org/doc/249071

ER -

## References

top- [1] F. Beukers, A note on the irrationality of ζ(2) and ζ(3). Bull. London Math. Soc.11 (1979), 268-272. Zbl0421.10023
- [2] L.A. Gutnik, The irrationality of certain quantities involving ζ(3). Acta Arith.42 (1983), 255-264. Zbl0474.10026
- [3] Yu L. Luke, Mathematical functions and their approximations. Academic Press, New York, 1975. Zbl0318.33001MR501762
- [4] YU. Nesterenko, A few remarks on ζ(3). Math. Notes59 (1996), 625-636. Zbl0888.11028
- [5] T. Hessami- Pilerhood, Linear independence of vectors with polylogarithmic coordinates. Vestnik Moscow University Ser.1 (1999), no6, 54-56. Zbl0983.11044MR1735148
- [6] T. Rivoal, La fonction Zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs. C. R. Acad. Sci. Paris331 (2000), 267-270. Zbl0973.11072MR1787183
- [7] L.J. Slater, Generalized hypergeometric functions. Cambridge Univ. Press, 1966. Zbl0135.28101MR201688
- [8] E.T. Whittaker, G.N. Watson, A course of modern analysis. CambdidgeUniversity Press, 1927. Zbl45.0433.02MR1424469JFM53.0180.04
- [9] V.V. Zudilin, On irrationality of values of Riemann zeta function. Izvestia of Russian Acad. Sci.66, 2002, 1-55. Zbl1114.11305MR1921809

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.