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1
Content available remote

Imaginary quadratic fields whose Iwasawa λ-invariant is equal to 1

100%
Byeon D.
Acta Arithmetica
|
2005
|
tom 120
|
nr 2
145-152
2
Content available remote

A note on class number 1 criteria for totally real algebraic number fields

100%
Byeon D.
Acta Arithmetica
|
2001
|
tom 100
|
nr 3
291-295
3
Content available remote

A note on basic Iwasawa λ-invariants of imaginary quadratic fields and congruence of modular forms

100%
Byeon D.
Acta Arithmetica
|
1999
|
tom 89
|
nr 3
295-299
4
Content available remote

Indivisibility of class numbers of imaginary quadratic function fields

100%
Byeon D.
Acta Arithmetica
|
2008
|
tom 132
|
nr 4
373-376
5
Content available remote

Indivisibility of special values of Dedekind zeta functions of real quadratic fields

100%
Byeon D.
Acta Arithmetica
|
2003
|
tom 109
|
nr 3
231-235
6
Content available remote

Ranks of quadratic twists of an elliptic curve

88%
Byeon D.
Acta Arithmetica
|
2004
|
tom 114
|
nr 4
391-396
7
Content available remote

Optimal curves differing by a 5-isogeny

64%
Byeon D., Kim T.
Acta Arithmetica
|
2014
|
tom 165
|
nr 4
351-359
EN
For i = 0,1, let $E_i$ be the $X_i(N)$-optimal curve of an isogeny class 𝓒 of elliptic curves defined over ℚ of conductor N. Stein and Watkins conjectured that E₀ and E₁ differ by a 5-isogeny if and only if E₀ = X₀(11) and E₁ = X₁(11). In this paper, we show that this conjecture is true if N is square-free and is not divisible by 5. On the other hand, Hadano conjectured that for an elliptic curve E defined over ℚ with a rational point P of order 5, the 5-isogenous curve E' := E/⟨P⟩ has a rational point of order 5 again if and only if E' = X₀(11) and E = X₁(11). In the process of the proof of Stein and Watkins's conjecture, we show that Hadano's conjecture is not true.
8
Content available remote

Optimal curves differing by a 3-isogeny

64%
Byeon D., Yhee D.
Acta Arithmetica
|
2013
|
tom 158
|
nr 3
219-227
EN
Stein and Watkins conjectured that for a certain family of elliptic curves E, the X₀(N)-optimal curve and the X₁(N)-optimal curve of the isogeny class 𝓒 containing E of conductor N differ by a 3-isogeny. In this paper, we show that this conjecture is true.
9
Content available remote

Mollin's conjecture

51%
Byeon D., Kim M., Lee J.
Acta Arithmetica
|
2007
|
tom 126
|
nr 2
99-114
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