Titles and Short Summaries of the Talks

22 Algebra
Final: 2013/2/7
55 Soichi Ikeda (Nagoya Univ.) ∗ On an alternating series representation of real numbers · · · · · · · · · · · · · 10
Summary: We introduce an algorithm which represent any real number as an alternating series
of rational numbers. That algorithm is a generalization of the alternating-Sylvester series and has
the same properties as that. In addition, we construct the real numbers by our alternating series
representation. Our method is similar to that of Arnold Knopfmacher and John Knopfmacher.
However, our proofs of the algebraic properties of the real numbers are achieved by a general lemma.
56 Soichi Ikeda (Nagoya Univ.)
Kaneaki Matsuoka (Nagoya Univ.)
Yoshikazu Nagata (Nagoya Univ.)
The mean values of Euler–Zagier double zeta function · · · · · · · · · · · · · · 10
Summary: Let s1 = σ1 + it and s2 = σ2 + it with σ1, σ2, t ∈ R. For certain σ1 and σ2, we prove
the mean value theorems for Euler double zeta-function ζ2(s1, s2). Our results suggest the existence
of an analogue of the critical line for ζ2(s1, s2).
57 Tomoya Machide (Kinki Univ.) ♯ Restricted sum formulas for double zeta values of even weight and
Ramanujan’s identity for Bernoulli numbers · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We give some restricted sum formulas for double zeta values of even weight. We also
prove that an obtained restricted sum formula yields Ramanujan’s identity for sums of products of
Bernoulli numbers with a gap of 6, and vice versa.
58 Yasuo Ohno (Kinki Univ.) ♯ On 2 and 3-orders of di-Bernoulli numbers · · · · · · · · · · · · · · · · · · · · · · · · 10
Mika Sakata (Kinki Univ.)
Summary: Poly-Bernoulli numbers were introduced and studied by M. Kaneko as a generalization
of classical Bernoulli numbers. He clarified the p-divisibility of denominators of di-Bernoulli
numbers. We plan to talk about 2 and 3-orders of di-Bernoulli numbers.
59 Tomoya Machide (Kinki Univ.) ♯ On a parameterized sum formula for quadruple zeta values · · · · · · · · · · 10
Summary: We give a parameterized generalization of the sum formula for quadruple zeta values.
The generalized formula has four parameters, and is invariant under a cyclic group of order four.
As applications, we also obtain weighted sum formulas for quadruple zeta values, which contain
some known and new results.
60 Takao Komatsu (Hirosaki Univ.) ♯
Ken Kamano (Osaka Inst. of Tech.)
Poly-Cauchy polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We introduce the poly-Cauchy polynomials which generalize the classical Cauchy
polynomials and numbers, and investigate their arithmetical properties. These polynomials are
considered as an analogue of poly-Bernoulli polynomials that generalize classical Bernoulli polyno-
mials and numbers. Moreover, we consider the zeta functions which interpolate the poly-Cauchy
polynomials. The values of these functions at positive integers can be expressed by using the
polylogarithm function or the truncated multiple zeta star values.