2 3 Ja n 20 06 MULTIPLE ZETA VALUES AND ROTA – BAXTER ALGEBRAS ( DEDICATED TO PROFESSOR MELVYN NATHANSON FOR HIS 60 TH BIRTHDAY )
نویسنده
چکیده
We study multiple zeta values and their generalizations from the point of view of Rota–Baxter algebras. We obtain a general framework for this purpose and derive relations on multiple zeta values from relations in Rota–Baxter algebras.
منابع مشابه
M ar 2 00 5 ROTA - BAXTER ALGEBRAS , DENDRIFORM ALGEBRAS AND POINCARÉ - BIRKHOFF - WITT THEOREM
Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double shuffle relations for multiple zeta values. The interest in the non-commutative setting arised in connection with the work of Connes and Kreimer on t...
متن کامل2 00 5 Rota - Baxter Algebras , Dendriform Algebras and Poincaré - Birkhoff - Witt Theorem
Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double shuffle relations for multiple zeta values. The interest in the non-commutative setting arose in connection with the work of Connes and Kreimer on th...
متن کاملRota–baxter Algebras in Renormalization of Perturbative Quantum Field Theory
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota–Baxter algebras enters the scene. In this note we revi...
متن کاملar X iv : m at h / 00 10 14 0 v 1 [ m at h . Q A ] 1 3 O ct 2 00 0 RELATIONS OF MULTIPLE ZETA VALUES AND THEIR ALGEBRAIC EXPRESSION
We establish a new class of relations among the multiple zeta values ζ(k1, . . . , kl) = ∑ n1>···>nl≥1 1 n k1 1 · · ·n kl k , which we call the cyclic sum identities. These identities have an elementary proof, and imply the “sum theorem” for multiple zeta values. They also have a succinct statement in terms of “cyclic derivations” as introduced by Rota, Sagan and Stein. In addition, we discuss ...
متن کاملA Riemann zeta stochastic process
and thus be represented (for σ > 1 ) as a product of terms of the form exp(a(eibt − 1)), each of which is the characteristic function of a Poisson random variable with intensity a and values in the lattice kb, k = 0, 1, 2, . . . . Cf. Gnedenko and Kolmogorov [6, p. 75]. Faced with a family of “zeta distributions” indexed by parameter σ > 1 , one is led to ask for joint distributions, i.e., for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006