• Korean Journal of Mathematics
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• 제24권3호
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• pp.331-334
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• 2016

We give an explicit formula for the computation of Iwa-sawa ${\lambda}$-invariants and an example of the computation using our method.

• 대한수학회보
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• 제49권1호
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• pp.155-163
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• 2012

Let E be an elliptic curve over $\mathbb{Q}$. Using Iwasawa theory, we give what seems to be the first general upper bound for the order of vanishing of the p-adic L-function at s = 0, and the $\mathbb{Z}_p$-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes p.

• 대한수학회지
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• 제45권2호
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• pp.435-453
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• 2008

In this paper, by using q-deformed bosonic p-adic integral, we give $\lambda$-Bernoulli numbers and polynomials, we prove Witt's type formula of $\lambda$-Bernoulli polynomials and Gauss multiplicative formula for $\lambda$-Bernoulli polynomials. By using derivative operator to the generating functions of $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, we give Hurwitz type $\lambda$-zeta functions and Dirichlet's type $\lambda$-L-functions; which are interpolated $\lambda$-Bernoulli polynomials and generalized $\lambda$-Bernoulli numbers, respectively. We give generating function of $\lambda$-Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and $\lambda$-Bernoulli polynomials and ordinary Bernoulli numbers of order r and $\lambda$-Bernoulli numbers, respectively. We also study on $\lambda$-Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define $\lambda$-partial zeta function and interpolation function.