Levels 11 and 23

Shaun Cooper
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Shaun Cooper: Massey University, Institute of Natural and Mathematical Science

Chapter Chapter 11 in Ramanujan's Theta Functions, 2017, pp 553-570 from Springer

Abstract: Abstract The theta functions ∑ m = − ∞ ∞ ∑ n = − ∞ ∞ q m 2 + m n + 3 n 2 , $$\sum _{m=-\infty }^{\infty }\sum _{ n=-\infty }^{\infty }q^{m^{2}+mn+3n^{2} },$$ ∑ m = − ∞ ∞ ∑ n = − ∞ ∞ q m 2 + m n + 6 n 2 and ∑ m = − ∞ ∞ ∑ n = − ∞ ∞ q 2 m 2 + m n + 3 n 2 $$\sum _{m=-\infty }^{\infty }\sum _{ n=-\infty }^{\infty }q^{m^{2}+mn+6n^{2} }\quad \mbox{ and}\quad \sum _{m=-\infty }^{\infty }\sum _{ n=-\infty }^{\infty }q^{2m^{2}+mn+3n^{2} }$$ are used to develop theories for levels 11 and 23 that are analogues of theorems in Chapters 5–10

Date: 2017
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DOI: 10.1007/978-3-319-56172-1_12

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