Vectorial Drinfeld modular forms over Tate algebras
In this paper, we develop the theory of vectorial modular forms with values in Tate algebras introduced by the first author, in a very special case (dimension two, for a very particular representation of Γ:=GL2(Fq[θ])Γ:=GL2(𝔽q[𝜃])<math display="inline" overflow="scroll" altimg...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
26 January 2018
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| In: |
International journal of number theory
Year: 2018, Volume: 14, Issue: 6, Pages: 1729-1783 |
| ISSN: | 1793-0421 |
| DOI: | 10.1142/S1793042118501063 |
| Online Access: | Verlag, Volltext: https://doi.org/10.1142/S1793042118501063 Verlag, Volltext: https://www.worldscientific.com/doi/abs/10.1142/S1793042118501063 
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| Author Notes: | Federico Pellarin, Rudolph B. Perkins |
| Summary: | In this paper, we develop the theory of vectorial modular forms with values in Tate algebras introduced by the first author, in a very special case (dimension two, for a very particular representation of Γ:=GL2(Fq[θ])Γ:=GL2(𝔽q[𝜃])<math display="inline" overflow="scroll" altimg="eq-00001.gif"><mi mathvariant="normal">Γ</mi><mspace width=".17em" class="thinspace"></mspace><mo class="MathClass-punc">:</mo><mo class="MathClass-rel">=</mo><mspace width=".17em" class="thinspace"></mspace><msub><mrow><mo class="qopname">GL</mo></mrow><mrow><mn>2</mn></mrow></msub><mo class="MathClass-open" stretchy="false">(</mo><msub><mrow><mi>𝔽</mi></mrow><mrow><mi>q</mi></mrow></msub><mo class="MathClass-open" stretchy="false">[</mo><mi>𝜃</mi><mo class="MathClass-close" stretchy="false">]</mo><mo class="MathClass-close" stretchy="false">)</mo></math>). Among several results that we prove here, we determine the complete structure of the modules of these forms, we describe their specializations at roots of unity and their connection with Drinfeld modular forms for congruence subgroups of ΓΓ<math display="inline" overflow="scroll" altimg="eq-00002.gif"><mi mathvariant="normal">Γ</mi></math> and we prove that the modules generated by these forms are stable under the actions of Hecke operators. |
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| Item Description: | Gesehen am 07.02.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1793-0421 |
| DOI: | 10.1142/S1793042118501063 |