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 Harder, Günter, 1938 author.
 Princeton, New Jersey : Princeton University Press, 2020
 Description
 Book — xi, 220 pages : illustrations ; 24 cm
 Summary

 Introduction
 The cohomology of GLn
 Analytic tools
 Boundary cohomology
 The strongly inner spectrum and applications
 Eisenstein cohomology
 Lfunctions
 HarishChandra modules over Z / by Günter Harder
 Archimedean intertwining operator / by Uwe Weselmann
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Shelved by Series title NO.203  Unknown 
2. A local trace formula for the GanGrossPrasad conjecture for unitary groups : the Archimedean case [2020]
 BeuzartPlessis, Raphaël, 1986 author.
 Paris, France : Société mathématique de France, 2020
 Description
 Book — ix, 305 pages ; 24 cm
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Shelved by Series title V.418  Unavailable In process 
 Brunault, François, author.
 Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2020
 Description
 Book — xv, 167 pages : illustrations ; 23 cm
 Summary

 1. Some basics
 2. Lehmer's problem
 3. Multivariate setting
 4. The dilogarithm
 5. Differential equations for families of Mahler measures
 6. Random walk
 7. The regulator map for $K_2$ of curves
 8. Deninger's method for multivariate polynomials
 9. The RogersZudilin method
 10. Modular regulators Appendix. Motivic cohomology and regulator maps References Author Index Subject index.
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QA161 .P59 B78 2020  Unknown 
 Beresnevich, Victor, 1971 author.
 Providence, RI : American Mathematical Society, [2020]
 Description
 Book — vii, 77 pages ; 26 cm
 Summary

 Part 1. Problems and main results
 Part 2. Developing techniques and establishing the main results Bibliography.
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Shelved by Series title NO.1276  Unknown 
 Bost, JeanBenoît, 1961 author.
 Cham, Switzerland : Birkhäuser, an imprint of Spinger Nature Switzerland AG, [2020]
 Description
 Book — xxxi, 374 pages ; 25 cm
 Summary

 Introduction. Hermitian vector bundles over arithmetic curves. Invariants of Hermitian vector bundles over arithmetic curves. Geometry of numbers and invariants. Countably generated projective modules and linearly compact Tate spaces over Dedekind rings. Ind and proHermitian vector bundles over arithmetic curves. Invariants of infinite dimensional Hermitian vector bundles: denitions and first properties. Summable projective systems of Hermitian vector bundles and niteness of invariants. Exact sequences of infinite dimensional Hermitian vector bundles and subadditivity of their invariants. Infinite dimensional vector bundles over smooth projective curves. Epilogue: formalanalytic arithmetic surfaces and algebraization. Appendix A. Large deviations and Cramer's theorem. Appendix B. Noncomplete discrete valuation rings and continuity of linear forms on prodiscrete modules. Appendix C. Measures on countable sets and their projective limits. Appendix D. Exact categories. Appendix E. Upper bounds on the dimension of spaces of holomorphic sections of line bundles over compact complex manifolds. Appendix F. John ellipsoids and finite dimensional normed spaces.
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QA242.6 .B67 2020  Unknown 
 Tsfasman, M. A. (Michael A.), 1954 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — x, 453 pages : illustration ; 27 cm.
 Summary

 Curves with many points. I: Modular curves Class field theory Curves with many points. II Infinite global fields Decoding: Some examples Sphere packings Codes from multidimensional varieties Applications Appendix: Some basic facts from Volume 1 Bibliography List of names Index.
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QA3 .A4 V.238  Unknown 
 Sivaramakrishnan, R., 1936 author.
 Second edition.  Boca Raton : CRC Press, Taylor & Francis Group, [2019]
 Description
 Book — xxxi, 411 pages : illustrations ; 25 cm
 Summary

 Section A  ELEMENTS OF THE THEORY OF NUMBERS. From Euclid to Lucas: Elementary theorems revisited. Solutions of Congruences, Primitive Roots. The Chinese Remainder Theorem. Mobius inversion. Quadratic Residues. Decomposition of a number as a sum of two or four squares. Dirichlet Algebra of Arithmetical Functions. Modular arithmetical functions. A generalization of Ramanujan sums. Ramanujan expansions of multiplicative arithmetic functions. Section B  SELECTED TOPICS IN ALGEBRA. On the uniqueness of a group of order r (r > 1). Quadratic Reciprocity in a finite group. Commutative rings with unity. Noetherian and Artinian rings. Section C  GLIMPSES OF THE THEORY OF ALGEBRAIC NUMBERS. Dedekind domains. Algebraic number fields. Section D  SOME ADDITIONAL TOPICS. Vaidyanathaswamy's classdivision of integers modulo r. Burnside's lemma and a few of its applications. On cyclic codes of length n over Fq. An Analogue of the Goldbach problem. Appendix A. Appendix B. Appendix C. Index.
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QA247 .S5725 2019  Unknown 
 Murty, Maruti Ram, author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — pages cm.
 Summary

 Introduction Cantor and infinity Axiomatic set theory Elementary number theory Computability and provability Hilbert's tenth problem Applications of Hilbert's tenth problem Hilbert's tenth problem over number fields Background material Bibliography Index.
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QA242 .M8945 2019  Unknown 
 LozanoRobledo, Álvaro, 1978 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — xv, 488 pages ; 27 cm.
 Summary

 Introduction Integers, polynomials, lines, and congruences: The integers The prime numbers Congruences Groups, rings, and fields Finite fields The theorems of Wilson, Fermat, and Euler Primitive roots Quadratic congruences and quadratic equations: An introduction to quadratic equations Quadratic congruences The HasseMinkowski theorem Circles, ellipses, and the sum of two squares problem Continued fractions Hyperbolas and Pell's equation Cubic equations and elliptic curves: An introduction to cubic equations Elliptic curves Bibliography Index.
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QA242.5 .L6945 2019  Unknown 
10. The plaid model [2019]
 Schwartz, Richard Evan, author.
 Princeton ; Oxford : Princeton University Press, 2019.
 Description
 Book — xii, 268 pages : illustrations ; 25 cm.
 Summary

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a selfcontained sequel to Richard Schwartz's Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites. Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called "the plaid model, " has a selfsimilar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics. The book includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.
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Shelved by Series title NO.198  Unknown 
 Lehman, J. L. (James Larry), 1957 author.
 Providence, Rhode Island : MAA Press, an imprint of the American Mathematical Society, [2019]
 Description
 Book — xiii, 394 pages : illustrations ; 24 cm.
 Summary

 Introduction: A brief review of elementary number theory Quadratic domains and ideals: Gaussian integers and sums of two squares Quadratic domains Ideals of quadratic domains Quadratic forms and ideals: Quadratic forms Correspondence between forms and ideals Positive definite quadratic forms: Class groups of negative discriminant Representations by positive definite forms Class groups of quadratic subdomains Indefinite quadratic forms: Continued fractions Class groups of positive discriminant Representations by indefinite forms Quadratic recursive sequences: Properties of recursive sequences Applications of quadratic recursive sequences Concluding remarks List of notation Index.
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QA247 .L41955 2019  Unknown 
 Li, W. C. Winnie (WenChing Winnie), author.
 Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, [2019]
 Description
 Book — vii, 95 pages : illustrations ; 26 cm.
 Summary

 Number theoretic zeta and $L$functions The Selberg zeta function $L$functions in geometry The Ihara zeta function Spectral graph theory Explicit constructions of Ramanujan graphs Artin $L$functions and prime distributions for graphs Zeta and $L$functions of complexes Bibliography Index.
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QA1 .R33 NO.129  Unknown 
 International Conference on padic Functional Analysis (14th : 2016 : Aurillac, France)
 [Providence, RI] : American Mathematical Society, [2018]
 Description
 Book — vi, 290 pages ; 26 cm.
 Summary

This book contains the proceedings of the 14th International Conference on $p$adic Functional Analysis, held from June 30July 5, 2016, at the Universite d'Auvergne, Aurillac, France. Articles included in this book feature recent developments in various areas of nonArchimedean analysis: summation of p adic series, rational maps on the projective line over Q p , nonArchimedean HahnBanach theorems, ultrametric Calkin algebras, G modules with a convex base, noncompact Trace class operators and Schattenclass operators in p adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in LeviCivita fields, ultrametric spectra of commutative nonunital Banach rings, classes of nonArchimedean Koethe spaces, p adic Nevanlinna theory and applications, and subcoordinate representation of p adic functions. Moreover, a paper on the history of p adic analysis with a comparative summary of nonArchimedean fields is presented. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in nonArchimedean analysis as well as a broad knowledge of some of the subareas of this exciting and fastdeveloping research area.
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QA241 .I585 2016  Unknown 
 Corvaja, Pietro, author.
 Cambridge, United Kingdom : Cambridge University Press, 2018.
 Description
 Book — x, 198 pages : illustrations ; 24 cm.
 Summary

 Notations and conventions Introduction
 1. Diophantine approximation and Diophantine equations
 2. Schmidt's subspace theorem and Sunit equations
 3. Integral points on curves and other varieties
 4. Diophantine equations with linear recurrences
 5. Some applications of the subspace theorem in transcendental number theory References Index.
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QA242 .C67 2018  Unknown 
 Cham, Switzerland : Springer, [2018]
 Description
 Book — xiv, 431 pages : illustrations (some color) ; 24 cm.
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Shelved by Series title V.2213  Unknown 
 Hutz, Benjamin, 1978 author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — xii, 313 pages : illustrations ; 26 cm.
 Summary

 Introduction Integers Modular arithmetic Quadratic reciprocity and primtive roots Secrets Arithmetic functions Algebraic numbers Rational and irrational numbers Diophantine equations Elliptic curves Dynamical systems Polynomials Bibliography List of algorithms List of notations Index.
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QA241 .H88 2018  Unknown 
17. Introduction to number theory [2018]
 Hill, Richard Michael, author.
 London ; Hackensack, NJ : World Scientific Publishing Europe Ltd., [2018]
 Description
 Book — xiv, 247 pages ; 23 cm.
 Summary

Textbook, with answers to some exercises.
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QA241 .H4845 2018  Unknown 
18. Lectures on logarithmic algebraic geometry [2018]
 Ogus, Arthur, author.
 Cambridge, United Kingdom : Cambridge University Press, 2018.
 Description
 Book — xviii, 539 pages : illustrations ; 24 cm.
 Summary

 1. The geometry of monoids
 2. Sheaves of monoids
 3. Logarithmic schemes
 4. Differentials and smoothness
 5. Betti and de Rham cohomology.
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QA565 .O38 2018  Unknown 
19. Nilpotent structures in ergodic theory [2018]
 Host, B. (Bernard), author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — x, 427 pages ; 27 cm.
 Summary

 Introduction
 Part 1. Basics: Background material Dynamical background Rotations Group extensions
 Part 2. Cubes: Cubes in an algebraic setting Dynamical cubes Cubes in ergodic theory The structure factors
 Part 3. Nilmanifolds and nilsystems: Nilmanifolds Nilsystems Cubic structures in nilmanifolds Factors of nilsystems Polynomials in nilmanifolds and nilsystems Arithmetic progressions in nilsystems
 Part 4. Structure theorems: The ergodic structure theorem Other structure theorems Relations between consecutive factors The structure theorem in a particular case The structure theorem in the general case
 Part 5. Applications: The method of characteristic factors Uniformity seminorms on $\ell^\infty$ and pointwise convergence of cubic averages Multiple correlations, good weights, and antiuniformity Inverse results for uniformity seminorms and applications The comparison method Bibliography Index of terms Index of symbols.
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QA3 .A4 V.236  Unknown 
20. Nuggets of number theory : a visual approach [2018]
 Nelsen, Roger B., author.
 Providence, Rhode Island : MAA Press, an imprint of the American Mathematical Society, [2018]
 Description
 Book — x, 153 pages : illustrations ; 26 cm.
 Summary

 Figurate numbers Congruence Diophantine equations Pythagorean triples Irrational numbers Fibonacci and Lucas numbers Perfect numbers Solutions to the exercises Bibliography Index.
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QA241 .N435 2018  Unknown 