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The aims of the present paper are: • to give other interesting relations among double zeta values, • to show that the structure of the Q-vector space of all relations among double zeta values of weight k is connected in many different ways with the structure of the space of modular forms Mk of weight k on the full modular group Γ1 = PSL(2, Z), and • to… (More)

Let p ≥ 5 be a prime number and Fp−1(τ) be the solution of the above differential equation for k = p−1 which is modular on SL2(Z) (such a solution exists and is unique up to a scalar multiple). For any zero τ0 in H of the form Fp−1(τ), the value of the jfunction at τ0 is algebraic and its reduction modulo (an extension of) p is a supersingular j-invariant… (More)

- Masanobu Kaneko
- 2000

A direct proof is given for Akiyama and Tanigawa’s algorithm for computing Bernoulli numbers. The proof uses a closed formula for Bernoulli numbers expressed in terms of Stirling numbers. The outcome of the same algorithm with different initial values is also briefly discussed. 1 The Algorithm In their study of values at non-positive integer arguments of… (More)

- Masanobu Kaneko, M. Koike
- 2008

The parameter k always stands for a non-negative integer or half an integer throughout the paper. This differential equation originates in the work [1] where in some cases (k ≡ 0, 4 mod 6) solutions which are modular on SL2(Z) were found and studied in connection with liftings of supersingular j-invariants of elliptic curves. The purpose of this paper is to… (More)

We give a formula for the coefficients of the YablonskiiVorob’ev polynomial. Also the reduction modulo a prime number of the polynomial is studied.

- Masanobu Kaneko
- 2007

We review several occurrences of poly-Bernoulli numbers in various contexts, and discuss in particular some aspects of relations of poly-Bernoulli numbers and special values of certain zeta functions, notably multiple zeta values.

- Masanobu Kaneko
- 2006

In this paper, we propose a conjectural generalization of the derivation relation for multiple zeta values. This extension was inspired by works of Alain Connes and Henri Moscovici on a certain Hopf algebra of transverse geometry [1], [2], and is thought of as a first attempt to materialize the suggestion given at the end of Section 7 in [4]. The multiple… (More)

- MASATAKA CHIDA, Masanobu Kaneko
- 2005

We give a criterion for a prime being ordinary for a modular form, by using the theta operator of Ramanujan.

- Hiroshi Yoshida, Yoshihiro Miwa, Masanobu Kaneko
- Applicable Algebra in Engineering, Communication…
- 2011

Starting from an egg, the multicell becomes a set of cells comprising a variety of types to serve functions. This phenomenon brings us a bio-motivated Lindenmayer system. To investigate conditions for a variety of cell types, we have constructed a stochastic model over Lindenmayer systems. This model considers interactive behaviors among cells, yielding… (More)