Nous étudions les fonctions génératrices des valeurs des fonctions polyzêta dans le cadre général. Ces fonctions génératrices établissent un lien entre les nombres polyzêta et les sommes d’Euler multiples, ce qui nous permet d’exprimer chaque valeur polyzêta en termes de sommes d’Euler multiples alternées, et notamment réduire la longueur des blocs de deux dans les sommes résultantes.
We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler sums, which allows us to express each multiple zeta star value in terms of multiple alternating Euler sums, and specifically, reduce the length of blocks of twos in the resulting sums.
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Mots clés : Multiple zeta star value, multiple zeta value, generating function, Euler sum
@article{JTNB_2019__31_2_343_0, author = {Hessami Pilehrood, Khodabakhsh and Hessami Pilehrood, Tatiana}, title = {Generating functions for multiple zeta star values}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {343--360}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {31}, number = {2}, year = {2019}, doi = {10.5802/jtnb.1084}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.1084/} }
TY - JOUR AU - Hessami Pilehrood, Khodabakhsh AU - Hessami Pilehrood, Tatiana TI - Generating functions for multiple zeta star values JO - Journal de théorie des nombres de Bordeaux PY - 2019 SP - 343 EP - 360 VL - 31 IS - 2 PB - Société Arithmétique de Bordeaux UR - http://archive.numdam.org/articles/10.5802/jtnb.1084/ DO - 10.5802/jtnb.1084 LA - en ID - JTNB_2019__31_2_343_0 ER -
%0 Journal Article %A Hessami Pilehrood, Khodabakhsh %A Hessami Pilehrood, Tatiana %T Generating functions for multiple zeta star values %J Journal de théorie des nombres de Bordeaux %D 2019 %P 343-360 %V 31 %N 2 %I Société Arithmétique de Bordeaux %U http://archive.numdam.org/articles/10.5802/jtnb.1084/ %R 10.5802/jtnb.1084 %G en %F JTNB_2019__31_2_343_0
Hessami Pilehrood, Khodabakhsh; Hessami Pilehrood, Tatiana. Generating functions for multiple zeta star values. Journal de théorie des nombres de Bordeaux, Tome 31 (2019) no. 2, pp. 343-360. doi : 10.5802/jtnb.1084. http://archive.numdam.org/articles/10.5802/jtnb.1084/
[1] Special values of multiple polylogarithms, Trans. Am. Math. Soc., Volume 353 (2001) no. 3, pp. 907-941 | DOI | MR | Zbl
[2] Mixed Tate motives over , Ann. Math., Volume 175 (2012) no. 2, pp. 949-976 | DOI | MR | Zbl
[3] Euler sums and contour integral representations, Exp. Math., Volume 7 (1998) no. 1, pp. 15-35 | DOI | MR | Zbl
[4] An alternative proof of a theorem of Zagier, J. Math. Anal. Appl., Volume 449 (2017) no. 1, pp. 168-175 | DOI | MR | Zbl
[5] Multiple zeta star values on 3-2-1 indices (2018) (https://arxiv.org/abs/1806.10510)
[6] New properties of multiple harmonic sums modulo and -analogues of Leshchiner’s series, Trans. Am. Math. Soc., Volume 366 (2014) no. 6, pp. 3131-3159 | MR | Zbl
[7] On -analogs of some families of multiple harmonic sums and multiple zeta star value identities, Commun. Number Theory Phys., Volume 10 (2016) no. 4, pp. 805-832 | DOI | MR | Zbl
[8] The algebra of multiple harmonic series, J. Algebra, Volume 194 (1997) no. 2, pp. 477-495 | DOI | MR | Zbl
[9] A family of multiple harmonic sum and multiple zeta star value identities, Mathematika, Volume 61 (2015) no. 1, pp. 63-71 | DOI | MR | Zbl
[10] Zeta stars, Commun. Number Theory Phys., Volume 2 (2008) no. 2, pp. 325-347 | DOI | MR | Zbl
[11] Evaluation of the multiple zeta values , Ann. Math., Volume 175 (2012) no. 2, pp. 977-1000 | DOI | MR | Zbl
[12] Identity families of multiple harmonic sums and multiple zeta star values, J. Math. Soc. Japan, Volume 68 (2016) no. 4, pp. 1669-1694 | DOI | MR | Zbl
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