• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.323-330
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• 2008

Some finiteness and non-existence results are proved of 2-dimensional mod 2 Galois representations of quadratic fields unramified outside 2.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1135-1140
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• 2016

Let A be an abelian variety over a global field K. We know [6, 7] that, in many cases, the average number of n-torsion points of A over various residue fields of K, takes the minimal possible value. In this article, we study several defect cases by calculating the number of Galois orbits.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.537-544
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• 2003

The non-existence is proved of continuous irreducible representations p : Gal(Q/Q) \longrightarrow GL$_2$(F$_{p}$) with Artin conductor N outside p for a few small values of p and N.N.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.173-176
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• 2007

The non-existence is proved of four-dimensional mod 2 semisimple representations of Gal ($\=\mathbb{Q}/\mathbb{Q}$) which are unramified outside 2.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.755-761
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• 2016

Let A be an abelian variety over a global field K. We show that, in "many" cases, Chen-Kuan's invariant M(A[n]), that is the average number of n-torsion points of A over various residue fields of K, has the minimal possible value.

• Korean Journal of Logic
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• v.10 no.1
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• pp.1-23
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• 2007

Dunn investigated algebras and semantics for negations in non-classical logics. This paper extends his investigation to dual negations, more exactly to duals to the negations in Dunn [3, 5]. I first survey and systematize the algebras of dual negations, i.e., (self-dual) subminimal negation, dual Galois negations, dual minimal negation, wB (or dual intuitionistic) negation, (self-dual) De Morgan negation, and (self-dual) ortho negation, based on partially ordered sets. I next provide dual-perp semantics for these (dual) negations. I finally give representations for them by using dual-perp semantics.