On rational functions with monodromy group M₁₁

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• 作者：Joachim Kö ; nig ^{joachim.koenig@mathematik.uni-wuerzburg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Galois theory ; Number fields ; Moduli spaces ; Monodromy groups
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：March-April 2017
• 年：2017
• 卷：79
• 期：part_P2
• 页码：372-383
• 全文大小：332 K

文摘

We compute new polynomials with Galois group n id="mmlsi1" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116000237&_mathId=si1.gif&_user=111111111&_pii=S0747717116000237&_rdoc=1&_issn=07477171&md5=c13ec30c0fcc0c2cf51c74b09cdf4494" title="Click to view the MathML source">M₁₁n>n class="mathContainer hidden">n class="mathCode">n>n>n> over n id="mmlsi103" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116000237&_mathId=si103.gif&_user=111111111&_pii=S0747717116000237&_rdoc=1&_issn=07477171&md5=ae592704f8ce6f511c73d4737ca1abfd" title="Click to view the MathML source">Q(t)n>n class="mathContainer hidden">n class="mathCode">n>n>n>. These polynomials stem from various families of covers of n id="mmlsi13" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116000237&_mathId=si13.gif&_user=111111111&_pii=S0747717116000237&_rdoc=1&_issn=07477171&md5=942828260d2955a8bcdc4a61719eefac" title="Click to view the MathML source">P¹Cn>n class="mathContainer hidden">n class="mathCode">n>n>n> ramified over at least 4 points. Each of these families has features that make a detailed study interesting. Some of the polynomials lead, via specialization, to number fields with very small discriminant or few ramified primes.