| dbo:abstract |
In number theory, the Stark conjectures, introduced by Stark and later expanded by Tate, give conjectural information about the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension K/k of algebraic number fields. The conjectures generalize the analytic class number formula expressing the leading coefficient of the Taylor series for the Dedekind zeta function of a number field as the product of a regulator related to S-units of the field and a rational number. When K/k is an abelian extension and the order of vanishing of the L-function at s = 0 is one, Stark gave a refinement of his conjecture, predicting the existence of certain S-units, called Stark units. Rubin and Cristian Dumitru Popescu gave extensions of this refined conjecture to higher orders of vanishing. (en) 数論において、スターク予想（英: Stark conjectures）とは、代数体のガロア拡大 K/k に付随するアルティン L 函数のテイラー展開の主要項の係数についての予想である。スターク予想はが で提示し、後日 Tateが拡張した。スターク予想は、数体のデデキントのゼータ函数のテイラー展開の主要項を表す解析的類数公式を一般化して、体の （S-units）に関連する単数基準と有理数との積として表すものである。スタークは K/k がアーベル拡大で、L 函数の s = 0 における位数 が 1 の場合について予想を精密化し、と呼ばれる S 単数の存在を予想した。 Rubin と は、この精密化された予想をさらに高次の位数へ拡張した。 (ja) |
| dbo:wikiPageExternalLink |
http://www.mathematics.jhu.edu/stark/ https://www.springer.com/birkhauser/mathematics/book/978-0-8176-3188-8 http://www.math.umass.edu/~dhayes/lecs.html https://arxiv.org/abs/2010.00657 https://web.archive.org/web/20120204044231/http:/www.math.umass.edu/~dhayes/lecs.html https://web.archive.org/web/20120426023029/http:/www.mathematics.jhu.edu/stark/ http://www.numdam.org/item%3Fid=AIF_1996__46_1_33_0 |
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Harold Stark (en) |
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Stark (en) |
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| rdfs:comment |
数論において、スターク予想（英: Stark conjectures）とは、代数体のガロア拡大 K/k に付随するアルティン L 函数のテイラー展開の主要項の係数についての予想である。スターク予想はが で提示し、後日 Tateが拡張した。スターク予想は、数体のデデキントのゼータ函数のテイラー展開の主要項を表す解析的類数公式を一般化して、体の （S-units）に関連する単数基準と有理数との積として表すものである。スタークは K/k がアーベル拡大で、L 函数の s = 0 における位数 が 1 の場合について予想を精密化し、と呼ばれる S 単数の存在を予想した。 Rubin と は、この精密化された予想をさらに高次の位数へ拡張した。 (ja) In number theory, the Stark conjectures, introduced by Stark and later expanded by Tate, give conjectural information about the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension K/k of algebraic number fields. The conjectures generalize the analytic class number formula expressing the leading coefficient of the Taylor series for the Dedekind zeta function of a number field as the product of a regulator related to S-units of the field and a rational number. When K/k is an abelian extension and the order of vanishing of the L-function at s = 0 is one, Stark gave a refinement of his conjecture, predicting the existence of certain S-units, called Stark units. Rubin and Cristian Dumitru Popescu gave extensions of thi (en) |
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スターク予想 (ja) Stark conjectures (en) |
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