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1. Heat Eisenstein series on SLn(C) [2009]
 Jorgenson, Jay.
 Providence, R.I. : American Mathematical Society, 2009.
 Description
 Book — vii, 127 p. ; 26 cm.
 Summary

A memoir that defines and studies multivariable Eisenstein series attached to heat kernels.
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Shelved by Series title NO.946  Unknown 
2. Algebra [2005]
 Lang, Serge, 19272005.
 Rev. 3rd ed., corr. printing.  New York : Springer, 2005.
 Description
 Book — xv, 914 p. : ill. ; 24 cm.
 Summary

 Foreword. Groups. Rings. Modules. Polynomials. Algebraic Equations. Galois Theory. Extensions of Rings. Transcendental Extensions. Algebraic Spaces. Noetherian Rings and Modules. Real Fields. Absolute Values. Matrices and Linear Maps. Representation of One Endomorphism. Structure of Bilinear Forms. The Tensor Product Semisimplicity. Representations of Finite Groups. The Alternating Product. General Homology Theory. Finite Free Resolutions. Appendices. Bibliography.
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QA154.3 .L3 2005  Unknown 
 Jorgenson, Jay.
 Berlin ; New York : Springer, c2005.
 Description
 Book — viii, 168 p. : ill. ; 24 cm.
 Summary

 GLn (R) actions on Posn(R). Measures, Integration, and Quadratic Model. Special Functions on Posn(R). Invariant Differential Operators on Posn(R). Poisson duality and zeta functions. Eisenstein Series: First Part. Geometric and Analytic Estimates. Eisenstein Series: Second Part.
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Shelved by Series title V.1868  Unknown 
4. Undergraduate algebra [2005]
 Lang, Serge, 19272005.
 3rd ed.  New York : Springer, c2005.
 Description
 Book — xi, 385 p. ; 25 cm.
 Summary

 Foreword. The Integers. Groups. Rings. Polynomials. Vector Spaces and Modules. Some Linear Groups. Field Theory. Finite Fields. The Real and Complex Numbers. Sets. Appendix. Index.
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QA152.2 .L36 2005  Unavailable Checked out  Overdue Request 
5. Algebra [2002]
 Lang, Serge, 19272005.
 Rev. 3rd ed.  New York : Springer, c2002.
 Description
 Book — xv, 914 p. : ill. ; 24 cm.
 Summary

 Foreword. Groups. Rings. Modules. Polynomials. Algebraic Equations. Galois Theory. Extensions of Rings. Transcendental Extensions. Algebraic Spaces. Noetherian Rings and Modules. Real Fields. Absolute Values. Matrices and Linear Maps. Representation of One Endomorphism. Structure of Bilinear Forms. The Tensor Product Semisimplicity. Representations of Finite Groups. The Alternating Product. General Homology Theory. Finite Free Resolutions. Appendices. Bibliography.
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QA154.3 .L3 2002  Unknown 
6. Introduction to differentiable manifolds [2002]
 Lang, Serge, 19272005.
 2nd ed.  New York : SpringerVerlag, c2002.
 Description
 Book — xi, 250 p. : ill. ; 24 cm.
 Summary

 Foreword. Acknowledgments. Differential Calculus. Manifolds. Vector Bundles. Vector Fields and Differential Equations. Operations on Vector Fields and Differential Forms. The Theorem of Frobenius. Metrics. Integration of Differential Forms. Stokes' Theorem. Applications of Stokes' Theorem.
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QA649 .L3 2002  Unknown 
7. Complex analysis [1999]
 Lang, Serge, 19272005.
 4th ed.  New York : Springer, c1999.
 Description
 Book — xiv, 485 p. : ill. ; 25 cm.
 Summary

 I: Basic Theory: Complex Numbers and Functions. Power Series. Cauchy's Theorem, First Part. Winding Numbers and Cauchy's Theorem. Applications of Cauchy's Integral Formula. Calculus of Residues. Conformal Mappings. Harmonic Functions. II: Geometric Function Theory: Schwarz Reflection. The Riemann Mapping Theorem. Analytic Continuation Along Curves. III: Various Analytic Topics: Applications of the Maximum Modulus Principle and Jensen's Formula. Entire and Meromorphic Functions. Elliptic Functions. The Gamma and Zeta Functions. The Prime Number Theorem.
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QA331 .L255 1999  Unknown 
8. Fundamentals of differential geometry [1999]
 Lang, Serge, 19272005.
 New York : Springer, c1999.
 Description
 Book — xvii, 535 p. : ill. ; 25 cm.
 Summary

 I.: General Differential Theory: Differential Calculus. Manifolds. Vector Bundles. Vector Fields and Differential Equations. Operations on Vector Fields and Differential Forms. The Theorem of Frobenius. II: Metrics, Covariant Derivatives and Riemannian Geometry: Metrics. Covariant Derivatives and Geodesics. Curvature. Jacobi Lifts and Tensorial Splitting of the Double Tangent Bundle. Curvature and the Variation Formula. An Example of Seminegative Curvature. Automorphisms and Symmetries. III: Volume Forms and Integration: Volume Forms. Integration of Differential Forms. Stokes' Theorem. Applications of Stokes' Theorem. Appendix: The Spectral Theorem.
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QA641 .L33 1999  Unknown 
9. Introduction to linear algebra [1986]
 Lang, Serge, 19272005.
 2nd ed.  New York : Springer, 1986.
 Description
 Book — viii, 293 p. : ill. ; 25 cm.
 Summary

 Vectors. Matrices and Linear Equations. Vector Spaces. Linear mappings. Composition and inverse mappings. Scalar Products and Orthogonality. Determinants. Eigenvectors and Eigenvalues. Answers to exercises. Index.
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QA251 .L25 1986  Unknown 
10. Undergraduate analysis [1997]
 Lang, Serge, 19272005.
 2nd ed.  New York : Springer, 1997.
 Description
 Book — xv, 642 p. : ill. ; 25 cm.
 Summary

 Review of Calculus: Sets and Mappings. Real Numbers. Limits and Continuous Functions. Differentiation. Elementary Functions. The Elementary Real Integral. Convergence: Normed Vector Spaces. Limits. Compactness. Series. The Integral in One Variable. Applications of the Integral: Fourier Series. Improper Integrals. The Fourier Integral. Calculus in Vector Spaces: Function on nSpace. The Winding Number and Global Potential Functions. Derivatives in Vector Spaces. Inverse Mapping Theorem. Ordinary Differential Equations. Multiple Integration: Multiple Integrals. Differential Forms. Appendix. Index.
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QA300 .L278 1997  Unknown 
11. Topics in cohomology of groups [1996]
 Rapport sur la cohomologie des groupes. English
 Lang, Serge, 19272005.
 Berlin ; New York : Springer, c1996.
 Description
 Book — vi, 226 p. ; 24 cm.
 Summary

The book is a mostly translated reprint of a report on cohomology of groups from the 1950s and 1960s, originally written as background for the ArtinTate notes on class field theory, following the cohomological approach. This report was first published (in French) by Benjamin. For this new English edition, the author added Tate's local duality, written up from letters which John Tate sent to Lang in 1958  1959. Except for this last item, which requires more substantial background in algebraic geometry and especially abelian varieties, the rest of the book is basically elementary, depending only on standard homological algebra at the level of first year graduate students.
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Shelved by Series title V.1625  Unknown 
12. Differential and Riemannian manifolds [1995]
 Lang, Serge, 19272005.
 New York : SpringerVerlag, c1995.
 Description
 Book — xiii, 364 p. : ill. ; 25 cm.
 Summary

This is the third version of a book on Differential Manifolds; in this latest expansion three chapters have been added on Riemannian and pseudoRiemannian geometry, and the section on sprays and Stokes' theorem have been rewritten. This text provides an introduction to basic concepts in differential topology, differential geometry and differential equations. In differential topology one studies classes of maps and the possibility of finding differentiable maps in them, and one uses differentiable structures on manifolds to determine their topological structure. In differential geometry one adds structures to the manifold (vector fields, sprays, a metric, and so forth) and studies their properties. In differential equations one studies vector fields and their integral curves, singular points, stable and unstable manifolds, and the like.
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QA614.3 .L35 1995  Unknown 
13. Algebraic number theory [1994]
 Lang, Serge, 19272005.
 2nd ed.  New York : SpringerVerlag, c1994.
 Description
 Book — xiii, 357 p. : ill. ; 25 cm.
 Summary

 Part I: General Basic Theory:
 1. Algebraic Integers.
 2. Completions.
 3. The Different and Discriminant.
 4. Cyclotomic Fields.
 5. Paralellotopes.
 6. The Ideal Function.
 7. Ideles and Adeles.
 8. Elementary Properties of the Zeta Function and Lseries. Part II: Class Field Theory:
 9. Norm Index Computations.
 10. The Artin Symbol, Reciprocity Law, and Class Field Theory.
 11. The Existence Theorem and Local Class Field Theory.
 12. Lseries Again. Part III: Analytic Theory:
 13. Functional Equation of the Zeta Function, Hecke's Proof.
 14. Functional Equation, Tate's Thesis.
 15. Density of Primes and Tauberian Theorem.
 16. The BrauerSiegel Theorem.
 17. Explicit Formulas. Bibliography. Index.
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Covers the basic material of classical algebraic number theory. This book gives the student the background useful for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms.
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QA247 .L32 1994  Unknown 
QA247 .L32 1994  Unknown 
 Goldfeld, D.
 Berlin ; New York : SpringerVerlag, c1994.
 Description
 Book — viii, 154 p. : ill. ; 24 cm.
 Summary

The theory of explicit formulae for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulae can be used to describe the quantitative behaviour of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulae and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory ad representation theory. Here, the hyperbolic 3manifolds are given as a significant example.
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Shelved by Series title V.1593  Unknown 
15. Algebra [1993]
 Lang, Serge, 19272005.
 3rd ed.  Reading, Mass. : AddisonWesley Pub. Co., c1993.
 Description
 Book — xv, 906 p. : ill. ; 24 cm.
 Summary

 I. THE BASIC OBJECTS OF ALGEBRA GROUPS. Groups. Rings. Modules. Polynomials. II. ALGEBRAIC EQUATIONS. Algebraic Extensions. Galois Theory. Extensions of Rings. Transcendental Extensions. Algebraic Spaces. Noetherian Rings and Modules. Real Fields. Absolute Values. III. LINEAR ALGEBRA AND REPRESENTATIONS. Matrices and Linear Maps. Representation of One Endomorphism. Structure of Bilinear Forms. The Tensor Product. Semisimplicity. Representations of Finite Groups. The Alternating Product. IV. HOMOLOGICAL ALGEBRA. General Homology Theory. Finite Free Resolution. Appendices.
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QA154.3 .L3 1993  Unknown 
QA154.3 .L3 1993  Unknown 
 Jorgenson, Jay.
 Berlin ; New York : SpringerVerlag, c1993.
 Description
 Book — 122 p.
 Summary

Analytic number theory and part of the spectral theory of operators (differential, pseudodifferential, elliptic, etc.) are being merged under a more general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact, or certain cases of noncompact, manifold. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and Lfunctions of number theory or representation theory and modular forms; Selberglike zeta functions; and to the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cramer's theorem and explicit formulas. The exposition is selfcontained (except for farreaching examples), requiring only standard knowledge of analysis.
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Shelved by Series title V.1564  Unknown 
17. Real and functional analysis [1993]
 Lang, Serge, 19272005.
 3rd ed.  New York : SpringerVerlag, 1993.
 Description
 Book — xiv, 580 p. ; 24 cm.
 Summary

This book is meant as a text for a firstyear graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus  linear algebra, differentiation, integration  but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with pointset topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the RiemannStjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. It includes several major spectral theorems of analysis, showing how one can extend to infinite dimensions certain results from finitedimensional linear algebra; a discussion of compact and Fredholm operators; and spectral theorems for Hermitian operators. The final part, on global analysis, provides an introduction to differentiable manifolds. The text includes worked examples and numerous exercises, which should be viewed as an integral part of the book. The organization of the book avoids long chains of logical interdependence, so that chapters are as independent as possible. This allows a course using the book to omit material from some chapters without compromising the exposition of material from later chapters.
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QA300 .L274 1993  Unknown 
18. Number theory III : diophantine geometry [1991]
 Berlin ; New York : SpringerVerlag, c1991.
 Description
 Book — xi, 296 p. ; 24 cm.
 Summary

Diophantine problems concern the solutions of equations in integers, rational numbers, or various generalizations. The book is an encyclopedic survey of diophantine geometry. For the most part no proofs are given, but references are given where proofs may be found. There are some exceptions, notably the proof for a large part of Faltings' theorems is given. The survey puts together, from a unified point of view, the field of diophantine geometry which has developed since the early 1950's, after its origins in Mordell, Weil and Siegel's papers in the 1920's. The basic approach is that of algebraic geometry, but examples are given which show how this approach deals with (and sometimes solves!) classical problems phrased in very elementary terms. For instance, the Fermat problem is not solved, but it is shown to fit in to two great structural approaches, so that it is not an isolated problem any more.
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QA242 .N85 1991  Unknown 
19. Topics in Nevanlinna theory [1990]
 Lang, Serge, 19272005.
 Berlin ; New York : SpringerVerlag, c1990.
 Description
 Book — 174 p. ; 24 cm.
 Summary

These are notes of lectures on Nevanlinna theory, in the classical case of meromorphic functions, and the generalization by CarlsonGriffith to equidimensional holomorphic maps using as domain space finite coverings of C resp. Cn. Conjecturally best possible error terms are obtained following a method of Ahlfors and Wong. This is especially significant when obtaining uniformity for the error term w.r.t. coverings, since the analytic yields case a strong version of Vojta's conjectures in the numbertheoretic case involving the theory of heights. The counting function for the ramified locus in the analytic case is the analogue of the normalized logarithmetic discriminant in the numbertheoretic case, and is seen to occur with the expected coefficient 1. The error terms are given involving an approximating function (type function) similar to the probabilistic type function of Khitchine in number theory. The leisurely exposition allows readers with no background in Nevanlinna Theory to approach some of the basic remaining problems around the error term. It may be used as a continuation of a graduate course in complex analysis, also leading into complex differential geometry.
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Shelved by Series title V.1433  Unknown 
20. Undergraduate algebra [1990]
 Lang, Serge, 19272005.
 2nd ed.  New York : SpringerVerlag, c1990.
 Description
 Book — xi, 367 p. : ill. ; 25 cm.
 Summary

 Foreword * The Integers * Groups * Rings * Polynomials * Vector Spaces and Modules * Some Linear Groups * Field Theory * Finite Fields * The Real and Complex Numbers * Sets * Appendix * Index.
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Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text.For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyder's proof of the MasonStothers polynomial abc theorem.About the First Edition:"The exposition is downtoearth and at the same time very smooth. The book can be covered easily in a oneyear course and can be also used in a oneterm course...the flavor of modern mathematics is sprinkled here and there. "Hideyuki Matsumura, Zentralblatt.
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QA152.2 .L36 1990  Unknown 