TABLE OF CONTENTS
INTRODUCTION 1
CHAPTER PAGE
I. PRELIMINARIES 7
§ 1. Quadratic lattices and their mass formulas 7
§2. Hermitian lattices and their mass formulas 8
II. GENERAL THEORY 11
§3. Lattices with non-trivial automorphisms whose minimal
polynomials are reducible 11
§4. Lattices with non-trivial automorphisms whose minimal
polynomials are irreducible 18
III. LOCAL DENSITIES 22
§5. Local densities of hermitian lattices 22
§6. List of quadratic lattices over 2 -adic integers and their
local densities 34
IV. ESTIMATIONS 38
§7. The estimation of
WR(2)/W(L)
41
§8. The estimation of u#(g)/a;(L), q ^ 2 55
§9. The estimation of wiR(q)/w(L) 64
V. PROOF OF THE THEOREMS 67
§ 10. Proof of the theorems 67
LIST OF REFERENCES 69
iii
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