In mathematics, the Schottky form or Schottky's invariant is a Siegel cusp form J of degree 4 and weight 8, introduced by Friedrich Schottky as a degree 16 polynomial in the Thetanullwerte of genus 4. He showed that it vanished at all Jacobian points (the points of the degree 4 Siegel upper half-space corresponding to 4-dimensional abelian varieties that are the Jacobian varieties of genus 4 curves). showed that it is a multiple of the difference θ4(E8 ⊕ E8) − θ4(E16) of the two genus 4 theta functions of the two 16-dimensional even unimodular lattices and that its divisor of zeros is irreducible. showed that it generates the 1-dimensional space of level 1 genus 4 weight 8 Siegel cusp forms.Ikeda showed that the Schottky form is the image of the Dedekind Delta function under the Ike
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| - Inom matematiken är Schottkys form eller Schottkys invariant en J av grad 4 och vikt 8 introducerad av Friedrich Schottky som ett 16:degradspolynom av av genus 4. Han bevisade att den försvinner vid alla Jacobiska punkter (punkterna av fjärdegradens Siegels övre halvplan korresponderande till fyrdimensionella abelska varieteter som är Jacobivarieteter av kurvor av genus 4). ) bevisade att den är en multipel av differensen θ4(E8 ⊕ E8) − θ4(E16) av två thetafunktioner av genus 4 av de två 16-dimensionella jämna unimodulära gittren och att dess nolldelare är irreducibelt. ) bevisade att den genererar det endimensionella rummet av Siegel-spetsformer av nivå 1, genus 4 och vikt 8. Ikeda bevisade att Schottkyformen är bilden av Dedekinds deltafunktion under Ikedalyftet. (sv)
- In mathematics, the Schottky form or Schottky's invariant is a Siegel cusp form J of degree 4 and weight 8, introduced by Friedrich Schottky as a degree 16 polynomial in the Thetanullwerte of genus 4. He showed that it vanished at all Jacobian points (the points of the degree 4 Siegel upper half-space corresponding to 4-dimensional abelian varieties that are the Jacobian varieties of genus 4 curves). showed that it is a multiple of the difference θ4(E8 ⊕ E8) − θ4(E16) of the two genus 4 theta functions of the two 16-dimensional even unimodular lattices and that its divisor of zeros is irreducible. showed that it generates the 1-dimensional space of level 1 genus 4 weight 8 Siegel cusp forms.Ikeda showed that the Schottky form is the image of the Dedekind Delta function under the Ike (en)
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| - In mathematics, the Schottky form or Schottky's invariant is a Siegel cusp form J of degree 4 and weight 8, introduced by Friedrich Schottky as a degree 16 polynomial in the Thetanullwerte of genus 4. He showed that it vanished at all Jacobian points (the points of the degree 4 Siegel upper half-space corresponding to 4-dimensional abelian varieties that are the Jacobian varieties of genus 4 curves). showed that it is a multiple of the difference θ4(E8 ⊕ E8) − θ4(E16) of the two genus 4 theta functions of the two 16-dimensional even unimodular lattices and that its divisor of zeros is irreducible. showed that it generates the 1-dimensional space of level 1 genus 4 weight 8 Siegel cusp forms.Ikeda showed that the Schottky form is the image of the Dedekind Delta function under the Ikeda lift. (en)
- Inom matematiken är Schottkys form eller Schottkys invariant en J av grad 4 och vikt 8 introducerad av Friedrich Schottky som ett 16:degradspolynom av av genus 4. Han bevisade att den försvinner vid alla Jacobiska punkter (punkterna av fjärdegradens Siegels övre halvplan korresponderande till fyrdimensionella abelska varieteter som är Jacobivarieteter av kurvor av genus 4). ) bevisade att den är en multipel av differensen θ4(E8 ⊕ E8) − θ4(E16) av två thetafunktioner av genus 4 av de två 16-dimensionella jämna unimodulära gittren och att dess nolldelare är irreducibelt. ) bevisade att den genererar det endimensionella rummet av Siegel-spetsformer av nivå 1, genus 4 och vikt 8. Ikeda bevisade att Schottkyformen är bilden av Dedekinds deltafunktion under Ikedalyftet. (sv)
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