Eta Products and Theta Series Identities

1. Dedekind’s Eta Function and Modular Forms
Günter Köhler

2. Eta Products
Günter Köhler

3. Eta Products and Lattice Points in Simplices
Günter Köhler

4. An Algorithm for Listing Lattice Points in a Simplex
Günter Köhler

5. Theta Series with Hecke Character
Günter Köhler

6. Groups of Coprime Residues in Quadratic Fields
Günter Köhler

7. Ideal Numbers for Quadratic Fields
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8. Eta Products of Weight 1/2 and 3/2

Günter Köhler

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
Günter Köhler

15. Levels N=p
3 and p
4 for Primes p

Günter Köhler

16. Levels N=pq with Primes 3≤p<q

Günter Köhler

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

Günter Köhler

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

Günter Köhler

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
Günter Köhler

26. Non-cuspidal Eta Products of Weight 1 for Level 12
Günter Köhler

27. Weight 1 for Fricke Groups Γ∗(q
3
p)
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28. Weight 1 for Fricke Groups Γ∗(2pq)
Günter Köhler

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)
Günter Köhler

31. Some More Levels 4pq with Odd Primes p≠q

Günter Köhler

Keywords: Mathematics, Number Theory, Algebraic Topology