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In this paper we are concerned with the monodromy of PicardFuchs differential equations associated with one-parameter families of CalabiYau threefolds. Our results show that in the hypergeometric… (More)
We study the automorphism groups of the reduction X 0 (N) × ¯ Fp of a modular curve X 0 (N) over primes p ∤ N .
Motivated by the relationship of classical modular functions and Picard–Fuchs linear differential equations of order 2 and 3, we present an analogous concept for equations of order 4 and 5.
Let Sw+2(Γ0(N)) be the vector space of cusp forms of weight w+2 on the congruence subgroup Γ0(N). We first determine explicit formulas for period polynomials of elements in Sw+2(Γ0(N)) by means of… (More)
In this paper, a model is developed for the evolution of plaques in arteries, which is one of the main causes for the blockage of blood flow. Plaque rupture and spread of torn-off material may cause… (More)
and then showing that bn/an converges to ζ(3) fast enough to ensure irrationality of ζ(3) (see ). Another remarkable discovery of Apéry is that an and bn satisfy the recursive relation (n + 2)un+2… (More)
Abstract. In this article, we consider the group F∞ 1 (N) of modular units on X1(N) that have divisors supported on the cusps lying over∞ of X0(N), called the ∞-cusps. For each positive integer N ,… (More)
play the central role. It can be shown that the Riemann zeta function can be analytically continued to the whole complex plane, except for a simple pole at s = 1. It has zeroes at −2n, n = 1, 2, . .… (More)
We consider the generalized Jacobian J̃0(N) of a modular curveX0(N) with respect to a reduced divisor given by the sum of all cusps on it. When N is a power of a prime ≥ 5, we exhibit that the group… (More)
Let ∆(T ) and E(T ) be the error terms in the classical Dirichlet divisor problem and in the asymptotic formula for the mean square of the Riemann zeta function in the critical strip, respectively.… (More)