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• W2248575259 abstract "In this expository article, we review some aspects of poly-Bernoulli numbers and related zeta functions. The poly-Bernoulli number is a generalization of the classical Bernoulli number using the polylogarithm series. Although its definition looks rather artificial at first glance, it has turned out recently that the poly-Bernoulli numbers of negative index have very nice combinatorial interpretations, and also they appear in special values of certain zeta functions. It may therefore be reasonable to seek arithmetic properties that may be involved with poly-Bernoulli numbers. The author made one such attempt with late Arakawa in the hope of finding a nice zeta function which connects poly-Bernoulli numbers with the so-called multiple zeta values, the subject of wide interest not only in number theory but also in numerous other branches such as topology, quantum groups, arithmetic geometry, mathematical physics etc. This work with Arakawa will be reviewed in §3, after recalling definitions and properties of poly-Bernoulli numbers in §2. In §4 we give some results and speculations concerning the “multiple harmonic sums mod p” and “multiple zeta-star values.” In the final section, §5, we discuss a different type of zeta function which also has some relation to poly-Bernoulli numbers as well as to certain generalized multiple zeta values. The author would like to take this opportunity to express his deep gratitude to late Professor Tsuneo Arakawa on the occasion of his sixtieth birthday, whose encouragement and interest at the early stage of the research on this topic greatly helped in developing the work further." @default.
• W2248575259 created "2016-06-24" @default.
• W2248575259 creator A5047107529 @default.
• W2248575259 date "2010-02-01" @default.
• W2248575259 modified "2023-09-25" @default.
• W2248575259 title "Poly-Bernoulli numbers and related zeta functions" @default.
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