The Siegel-Brauer theorem concerning parameters of algebraic number fields

Lavrik, A. F.

doi:10.1007/bf01093411

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λI? = θ(/Jδt(log|δ|) 2 )1

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1987

1998

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Cited by 3 publications

(3 citation statements)

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“…More recently Siegel [19] and Lavrik [13] have given general results from which an explicit constant c can be easily determined such that hR<c{\K\{\o%\Δ\) 2 .…”

Section: λI? = θ(/Jδt(log|δ|) 2 )mentioning

confidence: 99%

Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant

Barrucand¹,

Loxton²,

Williams³

1987

Pacific J. Math.

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“…More recently Siegel [19] and Lavrik [13] have given general results from which an explicit constant c can be easily determined such that hR<c{\K\{\o%\Δ\) 2 .…”

Section: λI? = θ(/Jδt(log|δ|) 2 )mentioning

confidence: 99%

Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant

Barrucand¹,

Loxton²,

Williams³

1987

Pacific J. Math.

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“…The author is deeply grateful to S. Louboutin for sending him reprints of his papers on class number bounds of imaginary abelian number fields and pointing out an error in the main result of [6], which was used in an earlier version of this paper. The author is also deeply grateful to Duncan Buell of the Center for Computing Sciences for doing a duplicate run of the long computer searches used in the proof of Theorem 2 and to L. C. Washington for sending the proof of Lemma 5 for d = 8.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Class number bounds and Catalan’s equation

Steiner

1998

Math. Comp.

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Abstract. We improve a criterion of Inkeri and show that if there is a solution to Catalan's equationwith p and q prime numbers greater than 3 and both congruent to 3 (mod 4), then p and q form a double Wieferich pair. Further, we refine a result of Schwarz to obtain similar criteria when only one of the exponents is congruent to 3 (mod 4). Indeed, in light of the results proved here it is reasonable to suppose that if q ≡ 3 (mod 4), then p and q form a double Wieferich pair.

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“…Let R K be the regulator of AT. By [10], [4,Corollary] there is a unit e in O K such that max{//(e;c), H(€y), H(e)} < exp{C 2…”

Section: Lemma 3 Assume D > 2 Let a B Be Two Non-zero Elements Of mentioning

confidence: 99%

Integer points on algebraic curves with exceptional units

Poulakis

1997

J Aust Math Soc A

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The Siegel-Brauer theorem concerning parameters of algebraic number fields

Cited by 3 publications

References 1 publication

Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant

Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant

Class number bounds and Catalan’s equation

Integer points on algebraic curves with exceptional units

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