Fetching the paper…
Reading the bibliography…
This paper deals with a multiple version of zeta- and L-functions both in the complex case and in the p-adic case: [I] Our motivation in the complex case is to find suitable rigorous meaning of the values of multivariable multiple zeta-functions (MZFs) at non-positive integer points.
G. Frobenius, Über die Bernoullischen Zahlen und die Eulerschen Polynome , Preuss. Akad. Wiss. Sitzungsber (1910), no. 2, 809–847
1910
Earlier work this paper cites.
T. Kubota and H. W. Leopoldt, Eine p p -adische Theorie der Zetawerte I. Einführung der p p -adischen Dirichletschen L L -Funktionen , J. reine angew. Math. 214/215
1964
Earlier work this paper cites.
K. Iwasawa, On p p -adic L L -functions , Ann. of Math. (2) 89
1969
Earlier work this paper cites.
Y. Amice and J. Fresnel, Fonctions zêta p p -adiques des corps de nombres abéliens réels , Acta Arith. 20
1972
Earlier work this paper cites.
by same author, Lectures on p p -adic L L -functions , Princeton University Press, Princeton, N.J., 1972. Annals of Mathematics Studies, No. 74
1972
Earlier work this paper cites.
J.-P. Serre, Formes modulaires et functions zêta p p -adiques , Lecture Notes in Math., 350
1973
Earlier work this paper cites.
T. Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers , J. Fac. Sci. Univ. Tokyo, Sect. IA, Math. 23
1976
Earlier work this paper cites.
J. Coates, P P -adic L L -functions and Iwasawa’s theory , Proceedings of the 1975 Durham Symposium, pp. 269–353, Academic Press, London-New York, 1977
1977
Earlier work this paper cites.
D. Barsky, Fonctions zêta p p -adiques d’une classe de rayon des corps de nombres totalement réels , Groupe de travail d’analyse ultramétrique 5
1978
Earlier work this paper cites.
P. Cassou-Noguès, Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p p -adiques , Invent. Math. 51
1979
Earlier work this paper cites.
N. Koblitz, A new proof of certain formulas for p p -adic L L -functions , Duke Math. J. 46
1979
Earlier work this paper cites.
P. Deligne and K. A. Ribet, Values of abelian L L -functions at negative integers over totally real fields , Invent. Math. 59
1980
Earlier work this paper cites.
by same author, p p -adic Analysis: A Short Course on Recent Work , London Mathematical Society Lecture Note Series, 46
1980
Earlier work this paper cites.
J. Fresnel and M. van der Put, Géométrie analytique rigide et applications , Progress in Mathematics 18
1981
Earlier work this paper cites.
H. Imai, On the construction of p p -adic L L -functions , Hokkaido Math. J. 10
1981
Earlier work this paper cites.
R. Coleman, Dilogarithms, regulators and p p -adic L L -functions , Invent. Math. 69
1982
Earlier work this paper cites.
S. Bosch, U. Güntzer, and R. Remmert, Non-Archimedean analysis. A systematic approach to rigid analytic geometry , Grundlehren der Mathematischen Wissenschaften, 261
1984
Cited alongside, same era.
H. Hida, Elementary theory of L L -functions and Eisenstein series , London Mathematical Society Student Texts, 26
1993
Cited alongside, same era.
D. Essouabri, Singularités des séries de Dirichlet associées à des polynômes de plusieurs variables et applications à la théorie analytique des nombres , Thèse, Univ. Nancy I, 1995
1995
Cited alongside, same era.
P. Berthelot, Cohomologie rigide et cohomologie rigide à support propre, Première partie , preprint, Université de Rennes, 1996
1996
Cited alongside, same era.
M. Kaneko, Poly-Bernoulli numbers , J. Théor. Nombr. Bordeaux 9
1997
Cited alongside, same era.
K. Matsumoto and Y. Tanigawa, The analytic continuation and the order estimate of multiple Dirichlet series , J. Théor. Nombr. Bordeaux 15
2003
Later among the works it cites.
H. Furusho, p p -adic multiple zeta values. I. p p -adic multiple polylogarithms and the p p -adic KZ equation , Invent. Math. 155
2004
Later among the works it cites.
J. Coates, T. Fukaya, K. Kato, R. Sujatha, and O. Venjakob, The G L 2 GL_{2} main conjecture for elliptic curves without complex multiplication , Publ. Math. Inst. Hautes Études Sci. 101
2005
Later among the works it cites.
M. de Crisenoy, Values at T T -tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables , Compositio Math. 142
2006
Later among the works it cites.
K. Matsumoto and H. Tsumura, Generalized multiple Dirichlet series and generalized multiple polylogarithms , Acta Arith. 124
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
L. C. Washington, Introduction to Cyclotomic Fields , Second edition, Graduate Texts in Mathematics, 83
1997
Cited alongside, same era.
T. Arakawa and M. Kaneko, Multiple zeta values, poly-Bernoulli numbers, and related zeta functions , Nagoya Math. J. 153
1999
Cited alongside, same era.
A. Besser, Syntomic regulators and p-adic integration II: K 2 of curves , Israel J. Math. 120
2000
Cited alongside, same era.
C. Breuil, Intégration sur les variétés p p -adiques (d’aprés Coleman, Colmez) , Séminaire Bourbaki, Vol. 1998/99, Astérisque No. 266
2000
Cited alongside, same era.
J. Zhao, Analytic continuation of multiple zeta functions , Proc. Amer. Math. Soc. 128
2000
Cited alongside, same era.
S. Akiyama, S. Egami, and Y. Tanigawa, Analytic continuation of multiple zeta-functions and their values at non-positive integers , Acta Arith. 98
2001
Cited alongside, same era.
S. Akiyama and Y. Tanigawa, Multiple zeta values at non-positive integers , Ramanujan J. 5
2001
Cited alongside, same era.
2006
Later among the works it cites.
by same author, p p -adic multiple zeta values. II. Tannakian interpretations , Amer. J. Math. 129
2007
Later among the works it cites.
by same author, The analytic theory of multiple zeta-functions and its applications , Sugaku Expositions 23
2007
Later among the works it cites.
L. Guo and B. Zhang, Renormalization of multiple zeta values , J. Algebra 319
2008
Later among the works it cites.
Y. Komori, An integral representation of multiple Hurwitz-Lerch zeta functions and generalized multiple Bernoulli numbers , Q. J. Math. 61
2010
Later among the works it cites.
D. Manchon and S. Paycha, Nested sums of symbols and renormalized multiple zeta values , Int. Math. Res. Not. (2010), no. 24
2010
Later among the works it cites.
G. Yamashita, Bounds for the dimensions of p p -adic multiple L L -value spaces , Doc. Math. 2010, Extra volume: Andrei A. Suslin sixtieth birthday, pp. 687–723
2010
Later among the works it cites.
Y. Komori, K. Matsumoto, and H. Tsumura, Functional equations for double L L -functions and values at non-positive integers , Intern. J. Number Theory 7
2011
Later among the works it cites.
B. A. Tangedal and P. T. Young, On p-adic multiple zeta and log gamma functions , J. Number Theory 131
2011
Later among the works it cites.
T. Onozuka, Analytic continuation of multiple zeta-functions and the asymptotic behavior at non-positive integers , Funct. Approx. Comment. Math. 49
2013
Closest in time.