Apéry-type(inverse)binomial series have appeared prominently in the calculations of Feynman integrals in recent years.In their previous work,the authors showed that a few large classes of the non-alternating Ape...Apéry-type(inverse)binomial series have appeared prominently in the calculations of Feynman integrals in recent years.In their previous work,the authors showed that a few large classes of the non-alternating Ape′ry-type(inverse)central binomial series can be evaluated using colored multiple zeta values of level four(i.e.,special values of multiple polylogarithms at the fourth roots of unity)by expressing them in terms of iterated integrals.In this sequel,the authors will prove that for several classes of the alternating versions they need to raise the level to eight.Their main idea is to adopt hyperbolic trigonometric 1-forms to replace the ordinary trigonometric ones used in the non-alternating setting.展开更多
Cyclotomic multiple zeta values are generalizations of multiple zeta values.In this paper,we establish sum formulas for various kinds of cyclotomic multiple zeta values.As an interesting application,we show that the Q...Cyclotomic multiple zeta values are generalizations of multiple zeta values.In this paper,we establish sum formulas for various kinds of cyclotomic multiple zeta values.As an interesting application,we show that the Q-algebra generated by Riemann zeta values are contained in the Qalgebra generated by unit cyclotomic multiple zeta values of level N for any N≥2.展开更多
In this paper, we shall define the renormalization of the multiple q-zeta values （MqZV） which are special values of multiple q-zeta functions ζq （s1,..., Sd） when the arguments are all positive integers or all no...In this paper, we shall define the renormalization of the multiple q-zeta values （MqZV） which are special values of multiple q-zeta functions ζq （s1,..., Sd） when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang （Renormalization of Multiple Zeta Values, arxiv： math/0606076v3）. We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζq（S1,..., sd） （i.e., s1 ≤ 1）. Moreover, when q ↑ 1 our renormalizations agree with those of Guo and Zhang.展开更多
基金supported by the National Natural Science Foundation of China(No.12101008)the Natural Science Foundation of Anhui Province(No.2108085QA01)the Jacobs Prize from the Bishop’s School。
文摘Apéry-type(inverse)binomial series have appeared prominently in the calculations of Feynman integrals in recent years.In their previous work,the authors showed that a few large classes of the non-alternating Ape′ry-type(inverse)central binomial series can be evaluated using colored multiple zeta values of level four(i.e.,special values of multiple polylogarithms at the fourth roots of unity)by expressing them in terms of iterated integrals.In this sequel,the authors will prove that for several classes of the alternating versions they need to raise the level to eight.Their main idea is to adopt hyperbolic trigonometric 1-forms to replace the ordinary trigonometric ones used in the non-alternating setting.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12201642 and 12371327)the Natural Science Foundation of Hunan Province,China(Grant No.2023JJ40691)。
文摘Cyclotomic multiple zeta values are generalizations of multiple zeta values.In this paper,we establish sum formulas for various kinds of cyclotomic multiple zeta values.As an interesting application,we show that the Q-algebra generated by Riemann zeta values are contained in the Qalgebra generated by unit cyclotomic multiple zeta values of level N for any N≥2.
文摘In this paper, we shall define the renormalization of the multiple q-zeta values （MqZV） which are special values of multiple q-zeta functions ζq （s1,..., Sd） when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang （Renormalization of Multiple Zeta Values, arxiv： math/0606076v3）. We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζq（S1,..., sd） （i.e., s1 ≤ 1）. Moreover, when q ↑ 1 our renormalizations agree with those of Guo and Zhang.
