Eta Products and Theta Series Identities

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ISBN: 978-3-642-16151-3 (Print) 978-3-642-16152-0 (Online)

Table of contents (31 chapters)

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  1. Front Matter

    Pages I-XXI

  2. Theoretical background

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 3-30

      Dedekind’s Eta Function and Modular Forms

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      Book Chapter

      Pages 31-37

      Eta Products

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      Book Chapter

      Pages 39-54

      Eta Products and Lattice Points in Simplices

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      Book Chapter

      Pages 55-65

      An Algorithm for Listing Lattice Points in a Simplex

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      Book Chapter

      Pages 67-79

      Theta Series with Hecke Character

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      Book Chapter

      Pages 81-95

      Groups of Coprime Residues in Quadratic Fields

  3. Examples

    1. Front Matter

      Pages 97-97

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      Book Chapter

      Pages 99-112

      Ideal Numbers for Quadratic Fields

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      Book Chapter

      Pages 113-118

      Eta Products of Weight \(\frac{1}{2}\) and \(\frac{3}{2}\)

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      Book Chapter

      Pages 119-131

      Level 1: The Full Modular Group

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      Book Chapter

      Pages 133-153

      The prime level N=2

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      Book Chapter

      Pages 155-171

      The prime level N=3

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      Book Chapter

      Pages 173-186

      Prime levels N=p≥5

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      Book Chapter

      Pages 187-214

      Level N=4

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      Book Chapter

      Pages 215-221

      Levels N=p 2 with Primes p≥3

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      Book Chapter

      Pages 223-250

      Levels N=p 3 and p 4 for Primes p

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      Book Chapter

      Pages 251-265

      Levels N=pq with Primes 3≤p<q

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      Book Chapter

      Pages 267-290

      Weight 1 for Levels N=2p with Primes p≥5

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      Book Chapter

      Pages 291-304

      Level N=6

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      Book Chapter

      Pages 305-318

      Weight 1 for Prime Power Levels p 5 and p 6

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      Book Chapter

      Pages 319-346

      Levels p 2 q for distinct primes p≠2 and q

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