著者

Nobushige KUROKAWA Masato WAKAYAMA

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.62, no.1, pp.171-187, 2008 (Released:2008-05-22)

参考文献数

16

被引用文献数

5 7

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Deformations of the multiple gamma and sine functions with respect to their periods are studied. To describe such deformations explicitly, a new class of generalized gamma and sine functions are introduced. In particular, we study the deformations from the viewpoint of multiplication formulas and Raabe's integral formulas for these gamma and sine functions. This new class of gamma functions contains Milnor's type multiple gamma functions as a special case.

著者

Ryota UMEZAWA

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.74, no.2, pp.233-254, 2020 (Released:2020-12-15)

参考文献数

12

被引用文献数

1

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We introduce an iterated integral version of (generalized) log-sine integrals(iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-sine integrals. We also give a new method for obtaining relations among multiple zeta values, which uses iterated log-sine integrals, and give alternative proofs of several known results related to multiple zeta values and log-sine integrals.

著者

Michael E. HOFFMAN

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.69, no.2, pp.345-366, 2015 (Released:2015-10-13)

参考文献数

30

被引用文献数

19 41

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We present a number of results about (finite) multiple harmonic sums modulo a prime, which provide interesting parallels to known results about multiple zeta values (i.e. infinite multiple harmonic series). In particular, we prove a ‘duality' result for mod p harmonic sums similar to (but distinct from) that for multiple zeta values. We also exploit the Hopf algebra structure of the quasi-symmetric functions to perform calculations with multiple harmonic sums mod p, and obtain, for each weight n through nine, a set of generators for the space of weight-n multiple harmonic sums mod p. When combined with recent work, the results of this paper offer significant evidence that the number of quantities needed to generate the weight-n multiple harmonic sums mod p is the nth Padovan number (OEIS sequence A000931).

著者

Hitodakari KUROYAMA

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.56, no.2, pp.293-297, 2002 (Released:2006-07-06)

参考文献数

8

著者

Masaki KATO

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.76, no.2, pp.451-475, 2022 (Released:2022-10-11)

参考文献数

15

被引用文献数

2

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Komori, Matsumoto and Tsumura introduced a zeta function ζr (s, Δ) associated with a root system Δ. In this paper, we introduce a q-analogue of this zeta function, denoted by ζr (s, a, Δ; q), and investigate its properties. We show that a ‘Weyl group symmetric' linear combination of ζr (s, a, Δ; q) can be written as a multiple integral over a torus involving functions Ψs. For positive integers k, functions Ψk can be regarded as q-analogues of the periodic Bernoulli polynomials. When Δ is of type A2 or A3, the linear combinations can be expressed as the functions Ψk, which are q-analogues of explicit expressions of Witten's volume formula. We also introduce a two-parameter deformation of the zeta function ζr (s, Δ) and study its properties.

著者

Hisayoshi KUBOTA Hiroshi SUGITA

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.56, no.2, pp.391-404, 2002 (Released:2006-07-06)

参考文献数

9

被引用文献数

4 8

著者

Shinichi MOCHIZUKI

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.62, no.2, pp.293-400, 2008 (Released:2008-09-09)

参考文献数

21

被引用文献数

2 2

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We develop the theory of Frobenioids, which may be regarded as a category-theoretic abstraction of the theory of divisors and line bundles on models of finite separable extensions of a given function field or number field. This sort of abstraction is analogous to the role of Galois categories in Galo is theory or monoids in the geometry of log schemes. This abstract category-theoretic framework preserves many o f the important features of the classical theory of divisors and line bundles on models of finite separable extensions of a function field or number field such as the global degree of an arithmetic line bundle over a number field, but also exhibits interesting new phenomena, such as a ‘Frobenius endomorphism’ of the Frobenioid associated to a number field.

著者

Densuke SHIRAISHI

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.75, no.1, pp.95-113, 2021 (Released:2021-06-08)

参考文献数

12

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The ℓ-adic Galois polylogarithm is an arithmetic function on an absolute Galois group with values in ℓ-adic numbers, which arises from Galois actions on ℓ-adic étale paths on ℙ1\{0, 1, ∞}. In the present paper, we discuss a relationship between ℓ-adic Galois polylogarithms and triple ℓth power residue symbols in some special cases studied in a work of Hirano and Morishita [J. Number Theory 198 (2019), 211-238]. We show that a functional equation of ℓ-adic Galois polylogarithms by Nakamura and Wojtkowiak [Non-abelian Fundamental Groups and Iwasawa Theory. Cambridge University Press, 2012, pp. 258-310] implies a reciprocity law of triple ℓth power residue symbols.

著者

Kazuko MATSUMOTO

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.72, no.1, pp.107-121, 2018 (Released:2018-06-27)

参考文献数

22

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A. Takeuchi showed that the negative logarithm of the Fubini-Study boundary distance function of pseudoconvex domains in the complex projective space CPn, n ∈ N, is strictly plurisubharmonic and solved the Levi problem for CPn. His estimate from below of the Levi form is nowadays called the ‘Takeuchi's inequality.' In this paper, we give the ‘Takeuchi's equality,' i.e. an explicit representation of the Levi form of the negative logarithm of the Fubini-Study distance to complex submanifolds in CPn.

著者

Kento FUJITA Yasushi KOMORI

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.75, no.1, pp.149-167, 2021 (Released:2021-06-08)

参考文献数

12

被引用文献数

1

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We prove a congruence between symmetric multiple zeta-star values and multiple zeta-star values. This congruence together with Aoki and Ohno's relation, the sum formula and the generalized height-one duality for multiple zeta-star values directly lead to those for the symmetric counterparts.

著者

Kalyan CHAKRABORTY Azizul HOQUE Mohit MISHRA

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.74, no.1, pp.201-210, 2020 (Released:2020-07-15)

参考文献数

30

被引用文献数

1 5

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We obtain criteria for the class number of certain Richaud-Degert type real quadratic fields to be three. We also treat a couple of families of real quadratic fields of Richaud-Degert type that were not considered earlier, and obtain similar criteria for the class number of such fields to be two and three.

著者

Xiaohan WANG Jay MEHTA Shigeru KANEMITSU

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.74, no.2, pp.313-335, 2020 (Released:2020-12-15)

参考文献数

72

被引用文献数

1 2

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As has been pointed out by Chakraborty et al (Seeing the invisible: around generalized Kubert functions. Ann. Univ. Sci. Budapest. Sect. Comput. 47 (2018), 185-195), there have appeared many instances in which only the imaginary part—the odd part—of the Lerch zeta-function was considered by eliminating the real part. In this paper we shall make full use of (the boundary function aspect of) the q-expansion for the Lerch zeta-function, the boundary function being in the sense of Wintner (On Riemann's fragment concerning elliptic modular functions. Amer. J. Math. 63 (1941), 628-634). We may thus refer to this as the ‘Fourier series-boundary q-series', and we shall show that the decisive result of Yamamoto (Dirichlet series with periodic coefficients. Algebraic Number Theory. Japan Society for the Promotion of Science, Tokyo, 1977, pp. 275-289) on short character sums is its natural consequence. We shall also elucidate the aspect of generalized Euler constants as Laurent coefficients after a brief introduction of the discrete Fourier transform. These are rather remote consequences of the modular relation, i.e. the functional equation for the Lerch zeta-function or the polylogarithm function. That such a remote-looking subject as short character sums is, in the long run, also a consequence of the functional equation indicates the ubiquity and omnipotence of the Lerch zeta-function—and, a fortiori, the modular relation(S. Kanemitsu and H. Tsukada. Contributions to the Theory of Zeta-Functions: the Modular Relation Supremacy. World Scientific, Singapore, 2014).

著者

Abdelmejid BAYAD Yoshinori HAMAHATA

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.65, no.1, pp.15-24, 2011 (Released:2011-06-01)

参考文献数

9

被引用文献数

33 47

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In this paper we investigate special generalized Bernoulli polynomials that generalize classical Bernoulli polynomials and numbers. We call them poly-Bernoulli polynomials. We prove a collection of extremely important and fundamental identities satisfied by our poly-Bernoulli polynomials and numbers. These properties are of arithmetical nature.

著者

Katsuhisa MIMACHI Masatoshi NOUMI

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.70, no.2, pp.315-342, 2016 (Released:2016-10-13)

参考文献数

28

被引用文献数

1 5

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The systems of differential equations associated with the classical hypergeometric functions and the hypergeometric functions on the space of point configurations are investigated from the viewpoint of the twisted de Rham theory. In each case, it is proved that the integral of a certain multivalued function over an arbitrary twisted (or loaded) cycle satisfies the system of differential equations in question. The classical hypergeometric functions studied here include Appell's hypergeometric functions F1, F2, F3, F4, Lauricella's hypergeometric functions FA, FB, FC, FD, and the generalized hypergeometric function n+1Fn.

著者

Masaaki YOSHIDA

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.50, no.2, pp.493-512, 1996 (Released:2007-01-16)

参考文献数

12

被引用文献数

5 6