Eta Products and Theta Series Identities

1. Dedekind’s Eta Function and Modular Forms
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2. Eta Products
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3. Eta Products and Lattice Points in Simplices
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4. An Algorithm for Listing Lattice Points in a Simplex
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5. Theta Series with Hecke Character
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6. Groups of Coprime Residues in Quadratic Fields
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7. Ideal Numbers for Quadratic Fields
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8. Eta Products of Weight 1/2 and 3/2

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9. Level 1: The Full Modular Group
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10. The prime level N=2
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11. The prime level N=3
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12. Prime levels N=p≥5
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13. Level N=4
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14. Levels N=p
2 with Primes p≥3
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15. Levels N=p
3 and p
4 for Primes p

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16. Levels N=pq with Primes 3≤p<q

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17. Weight 1 for Levels N=2p with Primes p≥5
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18. Level N=6
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19. Weight 1 for Prime Power Levels p
5 and p
6

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

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21. Levels 4p for the Primes p=23 and 19
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22. Levels 4p for p=17 and 13
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23. Levels 4p for p=11 and 7
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24. Weight 1 for level N=20
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25. Cuspidal Eta Products of Weight 1 for Level 12
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26. Non-cuspidal Eta Products of Weight 1 for Level 12
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27. Weight 1 for Fricke Groups Γ∗(q
3
p)
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28. Weight 1 for Fricke Groups Γ∗(2pq)
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29. Weight 1 for Fricke Groups Γ∗(p
2
q
2)
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30. Weight 1 for the Fricke Groups Γ∗(60) and Γ∗(84)
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31. Some More Levels 4pq with Odd Primes p≠q

Günter Köhler

Avainsanat: Mathematics, Number Theory, Algebraic Topology