Abelian Varieties with Complex Multiplication and Modular Functions : : (PMS-46) / / Goro Shimura.
Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular funct...
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| Superior document: | Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package |
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1998 |
| Year of Publication: | 2016 |
| Language: | English |
| Series: | Princeton Mathematical Series
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| Online Access: | |
| Physical Description: | 1 online resource (232 p.) |
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| LEADER | 07512nam a22017775i 4500 | ||
|---|---|---|---|
| 001 | 9781400883943 | ||
| 003 | DE-B1597 | ||
| 005 | 20220131112047.0 | ||
| 006 | m|||||o||d|||||||| | ||
| 007 | cr || |||||||| | ||
| 008 | 220131t20161998nju fo d z eng d | ||
| 019 | |a (OCoLC)990526066 | ||
| 020 | |a 9781400883943 | ||
| 024 | 7 | |a 10.1515/9781400883943 |2 doi | |
| 035 | |a (DE-B1597)474350 | ||
| 035 | |a (OCoLC)979954593 | ||
| 040 | |a DE-B1597 |b eng |c DE-B1597 |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a nju |c US-NJ | ||
| 050 | 4 | |a QA564 | |
| 072 | 7 | |a MAT022000 |2 bisacsh | |
| 082 | 0 | 4 | |a 514.3 |2 23 |
| 100 | 1 | |a Shimura, Goro, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Abelian Varieties with Complex Multiplication and Modular Functions : |b (PMS-46) / |c Goro Shimura. |
| 264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2016] | |
| 264 | 4 | |c ©1998 | |
| 300 | |a 1 online resource (232 p.) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 0 | |a Princeton Mathematical Series | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory (1961) -- |t Notation and Terminology -- |t I. Preliminaries on Abelian Varieties -- |t II. Abelian Varieties with Complex Multiplication -- |t III. Reduction of Constant Fields -- |t IV. Construction of Class Fields -- |t V. The Zeta Function of an Abelian Variety with Complex Multiplication -- |t VI. Families of Abelian Varieties and Modular Functions -- |t VII. Theta Functions and Periods on Abelian Varieties -- |t Bibliography -- |t Supplementary References -- |t Index -- |t About the Author |
| 506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
| 520 | |a Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively. | ||
| 530 | |a Issued also in print. | ||
| 538 | |a Mode of access: Internet via World Wide Web. | ||
| 546 | |a In English. | ||
| 588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
| 650 | 0 | |a Abelian varieties. | |
| 650 | 0 | |a Modular functions. | |
| 650 | 7 | |a MATHEMATICS / Number Theory. |2 bisacsh | |
| 653 | |a Abelian extension. | ||
| 653 | |a Abelian group. | ||
| 653 | |a Abelian variety. | ||
| 653 | |a Absolute value. | ||
| 653 | |a Adele ring. | ||
| 653 | |a Affine space. | ||
| 653 | |a Affine variety. | ||
| 653 | |a Algebraic closure. | ||
| 653 | |a Algebraic equation. | ||
| 653 | |a Algebraic extension. | ||
| 653 | |a Algebraic number field. | ||
| 653 | |a Algebraic structure. | ||
| 653 | |a Algebraic variety. | ||
| 653 | |a Analytic manifold. | ||
| 653 | |a Automorphic function. | ||
| 653 | |a Automorphism. | ||
| 653 | |a Big O notation. | ||
| 653 | |a CM-field. | ||
| 653 | |a Characteristic polynomial. | ||
| 653 | |a Class field theory. | ||
| 653 | |a Coefficient. | ||
| 653 | |a Complete variety. | ||
| 653 | |a Complex conjugate. | ||
| 653 | |a Complex multiplication. | ||
| 653 | |a Complex number. | ||
| 653 | |a Complex torus. | ||
| 653 | |a Corollary. | ||
| 653 | |a Degenerate bilinear form. | ||
| 653 | |a Differential form. | ||
| 653 | |a Direct product. | ||
| 653 | |a Direct proof. | ||
| 653 | |a Discrete valuation ring. | ||
| 653 | |a Divisor. | ||
| 653 | |a Eigenvalues and eigenvectors. | ||
| 653 | |a Embedding. | ||
| 653 | |a Endomorphism. | ||
| 653 | |a Existential quantification. | ||
| 653 | |a Field of fractions. | ||
| 653 | |a Finite field. | ||
| 653 | |a Fractional ideal. | ||
| 653 | |a Function (mathematics). | ||
| 653 | |a Fundamental theorem. | ||
| 653 | |a Galois extension. | ||
| 653 | |a Galois group. | ||
| 653 | |a Galois theory. | ||
| 653 | |a Generic point. | ||
| 653 | |a Ground field. | ||
| 653 | |a Group theory. | ||
| 653 | |a Groupoid. | ||
| 653 | |a Hecke character. | ||
| 653 | |a Homology (mathematics). | ||
| 653 | |a Homomorphism. | ||
| 653 | |a Identity element. | ||
| 653 | |a Integer. | ||
| 653 | |a Irreducibility (mathematics). | ||
| 653 | |a Irreducible representation. | ||
| 653 | |a Lie group. | ||
| 653 | |a Linear combination. | ||
| 653 | |a Linear subspace. | ||
| 653 | |a Local ring. | ||
| 653 | |a Modular form. | ||
| 653 | |a Natural number. | ||
| 653 | |a Number theory. | ||
| 653 | |a Polynomial. | ||
| 653 | |a Prime factor. | ||
| 653 | |a Prime ideal. | ||
| 653 | |a Projective space. | ||
| 653 | |a Projective variety. | ||
| 653 | |a Rational function. | ||
| 653 | |a Rational mapping. | ||
| 653 | |a Rational number. | ||
| 653 | |a Real number. | ||
| 653 | |a Residue field. | ||
| 653 | |a Riemann hypothesis. | ||
| 653 | |a Root of unity. | ||
| 653 | |a Scientific notation. | ||
| 653 | |a Semisimple algebra. | ||
| 653 | |a Simple algebra. | ||
| 653 | |a Singular value. | ||
| 653 | |a Special case. | ||
| 653 | |a Subgroup. | ||
| 653 | |a Subring. | ||
| 653 | |a Subset. | ||
| 653 | |a Summation. | ||
| 653 | |a Theorem. | ||
| 653 | |a Vector space. | ||
| 653 | |a Zero element. | ||
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Mathematical Series eBook Package |z 9783110501063 |o ZDB-23-PMS |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Archive 1927-1999 |z 9783110442496 |
| 776 | 0 | |c print |z 9780691016566 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400883943 |
| 856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400883943 |
| 856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400883943/original |
| 912 | |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999 |c 1927 |d 1999 | ||
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