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二次型的算术理论（影印版）

样章
作者：
Burton W. Jones 著
定价：
99.00元
版面字数：
370.00千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2026-01-06
ISBN：
978-7-04-065968-9
物料号：
65968-00
出版时间：
2026-03-27
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
数论
暂无
  • 前辅文
  • I. Forms with real coefficients
    • 1. Fundamental notions
    • 2. A canonical form for congruence
    • 3. The determination of the index of a form
    • 4. Representation of one form by another
    • 5. Automorphs and the number of representations
    • 6. Summary
  • II. Forms with p-adic coefficients
    • 7. The definition and properties of p-adic numbers
    • 8. Congruences and p-adic numbers
    • 9. Congruence of forms in F(p)
    • 10. The Hilbert symbol
    • 11. Hasse's symbol cp(f)
    • 12. Some properties of cp(f) and kp(f)
    • 13. Evaluation of the Hasse symbol
    • 14. Zero forms
    • 15. The solvability of f=v
    • 16. Congruence of forms
    • 17. Representation of one form by another
    • 18. Universal forms
  • III. Forms with rational coefficients
    • 19. Congruence
    • 20. Equivalence and reduced forms
    • 21. The fundamental theorem on zero forms
    • 22. The fundamental theorem on rational congruence
    • 23. Representation of one form by another
  • IV. Forms with coefficients in R(p)
    • 24. Equivalence
    • 25. Canonical forms
    • 26. Representation of numbers by forms
    • 27. Equivalence of forms in R(p)
    • 28. Representation of one form by another and existence of forms with given invariants
    • 29. Zero forms and universal forms
    • 30. Automorphs and representations
    • 31. Binary forms
  • V. Genera and semi-equivalence
    • 32. Definitions
    • 33. Representation without essential denominator
    • 34. Existence of forms with integral coefficients and having given invariants
  • VI. Representations by forms
    • 35. Introduction
    • 36. Siegel's representation function
    • 37. Asymptotic results
    • 38. A representation function
  • VII. Binary forms
    • 39. Introduction
    • 40. Automorphs
    • 41. Representations by binary forms
    • 42. Ideals in a quadratic field
    • 43. A correspondence between ideal classes and classes of quadratic forms
    • 44. Composition of ideal classes and classes of forms
    • 45. Consequences of the composition of forms
    • 46. Genera
    • 47. Reduction of positive definite and zero binary forms
    • 48. Reduction of indefinite, non-zero, binary forms
    • 49. Class number
  • VIII. Ternary Quadratic Forms
    • 50. Numbers represented by ternary genera
    • 51. Numbers represented by forms
    • 52. The number of representations by ternary genera
  • Bibliography
  • Problems
  • Theorem Index
  • Index

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