Contents
Abstract ix
Introduction 1
Chapter 1. Definition of ˆ ω and statement of main result 5
Chapter 2. Deducing Theorem 1.2 from Theorem 2.1 and Proposition 2.2 11
Chapter 3. A determinant formula for ˆ ω 15
Chapter 4. An exact formula for Us(a, b) 19
Chapter 5. Asymptotic singularity and Newton’s divided difference operator 27
Chapter 6. The asymptotics of the entries in the U-part of M 37
Chapter 7. The asymptotics of the entries in the P -part of M
41
Chapter 8. The evaluation of det(M ) 49
Chapter 9. Divisibility of det(M ) by the powers of q ζ and q ζ−1 53
Chapter 10. The case q = 0 of Theorem 8.1, up to a constant multiple 57
Chapter 11. Divisibility of det(dM0) by the powers of
(xi xj ) ζ±1(yi yj ) ah 61
Chapter 12. Divisibility of det(dM0) by the powers of (xi
−zj)−ζ±1(yi
−wj) 67
Chapter 13. The proofs of Theorem 2.1 and Proposition 2.2 73
Chapter 14. The case of arbitrary slopes 75
Chapter 15. Random covering surfaces and physical interpretation 81
Appendix. A determinant evaluation 87
Bibliography 99
vii
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