Relations between cusp forms sharing Hecke eigenvalues

Relations between cusp forms sharing Hecke eigenvalues
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共享 Hecke 特征值的尖点形式之间的关系

DOI:
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发表时间:
2020
期刊:
Representation Theory: An Electronic Journal of the AMS
影响因子:
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通讯作者:
R. Raghunathan
R. Raghunathan
中科院分区:
--
文献类型:
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作者:
Dipendra Prasad;R. Raghunathan

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<p>本文考虑了当尖点形式的Hecke特征值集<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L Subscript n Baseline left-parenthesis double-struck upper A Subscript upper F Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">一</mml:mi> </mml:mrow> <mml:mi>F</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_n(mathbb {A}_F)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>包含在尖点形式的Hecke特征值集中,<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L Subscript m Baseline left-parenthesis double-struck upper A Subscript upper F Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>M</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">一</mml:mi> </mml:mrow> <mml:mi>F</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_m(mathbb {A}_F)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>为<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n less-than-or-equal-to m"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>M</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">n leq m</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.这个问题是密切相关的一个问题,有限维表示的一个抽象的群体,这也是我们认为在这项工作。</p>
<p>In this paper we consider the question of when the set of Hecke eigenvalues of a cusp form on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L Subscript n Baseline left-parenthesis double-struck upper A Subscript upper F Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">A</mml:mi> </mml:mrow> <mml:mi>F</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_n(mathbb {A}_F)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is contained in the set of Hecke eigenvalues of a cusp form on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G upper L Subscript m Baseline left-parenthesis double-struck upper A Subscript upper F Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">A</mml:mi> </mml:mrow> <mml:mi>F</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">GL_m(mathbb {A}_F)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n less-than-or-equal-to m"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>m</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">n leq m</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This question is closely related to a question about finite dimensional representations of an abstract group, which also we consider in this work.</p>
具有同源还原的阿贝尔簇
DOI: 10.5802/crmath.129
发表时间: 2020
期刊: Comptes rendus
影响因子: --
作者:
Khare, Chandreshekhar;Larsen, Michael:
通讯作者: Larsen, Michael: