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Higher Ramanujan Equations and Periods of Abelian Varieties
Softcover ISBN:  9781470460198 
Product Code:  MEMO/281/1391 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470473242 
Product Code:  MEMO/281/1391.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470460198 
eBook: ISBN:  9781470473242 
Product Code:  MEMO/281/1391.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $136.00 $102.00 
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Higher Ramanujan Equations and Periods of Abelian Varieties
Softcover ISBN:  9781470460198 
Product Code:  MEMO/281/1391 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470473242 
Product Code:  MEMO/281/1391.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470460198 
eBook ISBN:  9781470473242 
Product Code:  MEMO/281/1391.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $136.00 $102.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 281; 2023; 125 ppMSC: Primary 14; 37; 11

Table of Contents

Chapters

Introduction

Terminology and conventions

Acknowledgments

1. The arithmetic theory of the higher Ramanujan equations

1. Symplectic vector bundles over schemes

2. SymplecticHodge bases of principally polarized abelian schemes

3. Abelian schemes with real multiplication

4. The moduli stacks $\mathcal {B}_g$ and $\mathcal {B}_F$

5. The tangent bundles of $\mathcal {B}_g$ and $\mathcal {B}_F$; higher Ramanujan vector fields

6. Integral solution of the higher Ramanujan equations

7. Representability of $\mathcal {B}_g$ and $\mathcal {B}_F$ by a scheme

8. The case of elliptic curves: explicit equations

2. The analytic higher Ramanujan equations and periods of abelian varieties

9. Analytic families of complex tori, abelian varieties, and their uniformization

10. Analytic moduli spaces of complex abelian varieties with a symplecticHodge basis

11. The analytic higher Ramanujan equations

12. Values of $\varphi _g$ and $\varphi _F$; periods of abelian varieties

13. An algebraic independence conjecture on the values of $\varphi _F$

14. Grouptheoretic description of the higher Ramanujan vector fields

15. Zariskidensity of leaves of the higher Ramanujan foliation

A. GaussManin connection on some families of elliptic curves

Index of notation


Additional Material

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 Table of Contents
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Volume: 281; 2023; 125 pp
MSC: Primary 14; 37; 11

Chapters

Introduction

Terminology and conventions

Acknowledgments

1. The arithmetic theory of the higher Ramanujan equations

1. Symplectic vector bundles over schemes

2. SymplecticHodge bases of principally polarized abelian schemes

3. Abelian schemes with real multiplication

4. The moduli stacks $\mathcal {B}_g$ and $\mathcal {B}_F$

5. The tangent bundles of $\mathcal {B}_g$ and $\mathcal {B}_F$; higher Ramanujan vector fields

6. Integral solution of the higher Ramanujan equations

7. Representability of $\mathcal {B}_g$ and $\mathcal {B}_F$ by a scheme

8. The case of elliptic curves: explicit equations

2. The analytic higher Ramanujan equations and periods of abelian varieties

9. Analytic families of complex tori, abelian varieties, and their uniformization

10. Analytic moduli spaces of complex abelian varieties with a symplecticHodge basis

11. The analytic higher Ramanujan equations

12. Values of $\varphi _g$ and $\varphi _F$; periods of abelian varieties

13. An algebraic independence conjecture on the values of $\varphi _F$

14. Grouptheoretic description of the higher Ramanujan vector fields

15. Zariskidensity of leaves of the higher Ramanujan foliation

A. GaussManin connection on some families of elliptic curves

Index of notation
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