Spherical polynomials and the periods of a certain modular form

David Kramer

Type: Article

Publication Date: 1986-01-01

Citations: 4

DOI: https://doi.org/10.1090/s0002-9947-1986-0825724-0

Abstract

The space of cusp forms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S upper L Subscript 2 Baseline left-parenthesis bold upper Z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>S</mml:mtext> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>L</mml:mtext> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">Z</mml:mi> </mml:mrow> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">{\text {S}}{{\text {L}}_2}({\mathbf {Z}})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of weight <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2 k"> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>k</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">2k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is spanned by certain modular forms with rational periods.

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Transactions of the American Mathematical Society - View - PDF

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