Masanobu Kaneko

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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)
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)
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)
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)