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科学网-[转贴]西文数学书籍大全 4G多资源 - 0 views

  • Number theory : A Computational Introduction to Number Theory and Algebra - Victor Shoup A Concise Introduction to the Theory of Numbers- Baker A. A Course in Arithmetic (graduate level) - J. Serre A course in computational algebraic number theory - Cohen H. A Course in Number Theory and Cryptography 2 ed - Neal Koblitz A Course In Number Theory And Cryptography 2Ed - Koblitz N Advanced Number Theory - Cohn Algebra and number theory - Baker A. Algebraic Groups and Number Theory - Platonov & Rapinchuk Algebraic Number Theory - IYANAGA ALGEBRAIC NUMBER THEORY - MILNE Algorithmic Methods In Algebra And Number Theory - Pohst M Algorithmic number theory - Cohen H. Algorithmic number theory, vol. 1 Efficient algorithms - Bach E., Shallit J. An Explicit Approach To Elementary Number Theory - stein An Introduction to Conformal Field Theory [jnl article] - M. Gaberdiel AN INTRODUCTION TO THE THEORY OF NUMBERS - hardy & wright An Introduction to the Theory of Numbers - Leo Moser An introduction to the theory of numbers 5ed - Niven I., Zuckerman H.S., Montgomery H.L. Analytic number theory - Iwaniec H.,Kowalski E. Analytic Number Theory - Newman D.J. Analytic Number Theory- Jia & Matsumoto Arithmetic Theory of Elliptic Curves - J. Coates Computational Algebraic Number Theory - Pohst M E Computational excursions in analysis and number theory - Borwein P.
  • Only Problems Not Solutions - F. Smarandache Prime Numbers The Most Mysterious Figures in Math - D. Wells Problems In Algebraic Number Theory 2Ed - Murty M , Esmonde J SOlved and unsolved problems in Number Theory - Daniel Shanks Surfing on the Ocean of Numbers - H. Ibstedt Survey Of Diophantine Geometry - Serge Lang The elements of the theory of algebraic numbers - Hilbert.djv The Foundations of Arithmetic 2nd ed. revised - G. Frege The New Book Of Prime Number Records 3rd ed. - P. Ribenboim The Theory of algebraic numbers sec ed - Pollard H., Diamond H.G. the theory of functions and sets of natural numbers - Odifreddi, P Three Pearls of Number Theory - Khinchin Transcendental number theory - Baker A. Unsolved Problems In Number Theory 2 Ed - R K Guy.djv
  • Introduction to Modern Number Theory Fundamental Problems, Ideas and Theories 2nd Edition - Manin I., Panchishkin A Introduction to p-adic numbers and valuation theory- Bachman G. Introduction to the Theory of Numbers 4th ed. - G. Hardy, E. Wright Lectures on topics in algebraic number theory - Ghorpade Mainly Natural Numbers - Studies on Sequences - H. Ibstedt Math. problems and proofs combinatorics, number theory and geometry - B. Kisacanin Mathematical Problems And Proofs Combinatorics, Number Theory, and Geometry - Kluwer Academic My Numbers, My Friends - Popular Lectures on Number Theory My Numbers,My Friends Popular Lectures On Number Theory - Ribenboim Number Theory - Z.Borevitch, I. Shafarevich Number theory for beginners - Weil A. Number theory for computing - Yan S Y. Numerical Mathematics - A. Quarteroni, A. Sacco, F. Saleri Numerical Methods for Engineers and Scientists 2nd ed. - J. Hoffman Numerical Optimization - J. Nocedal, S. Wright Numerical Recipes in C - The Art Of Scientific Computing 2nd ed. Numerical Recipes in Fortran 77 2nd ed. Vol 1 Old And New Problems And Results In Combinatorial Number Theory - Erdos, P.&Graham, R.L
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  • Contributions to the Founding of the Theory of Transfinite Numbers - Georg Cantor Definitions, Solved And Unsolved Problems, Conjectures and Theorems, In Number Theory And Geometry - Smarandache F Elementary Methods in Number Theory - Nathanson M.B Elementary Number Theory - Clark Elementary Number Theory - David M. Burton Elementary Number Theory And Primality Tests Elementary Number Theory Notes - santos Elementary theory of numbers - Sierpinski W. Elliptic Curves - Notes for Math 679 - J. Milne, U. Michigan Elliptic Curves 2nd ed. - D. Husemoeller Geometric Theorems, Diophantine Equations and Arithmetic Functions - J. Sandor History of the theory of numbers Vol.2. - Dickson L.E. Introduction To Analytic Number Theory - Apostol
  • Ramanujan's Notebooks : Ramanujan's Notebooks vol 1 - B. Berndt.djv Ramanujan's Notebooks vol 2 - B. Berndt.djv Ramanujan's Notebooks vol 3 - B. Berndt.djv Ramanujan's Notebooks vol 4 - B. Berndt.djv Ramanujan's Notebooks vol 5 - B. Berndt.djv
arithwsun arithwsun

Szemeredi's theorem - 30 views

http://in-theory.blogspot.com/2006_05_28_archive.html in theory Saturday, June 03, 2006 Szemeredi's theorem Szemeredi's theorem on arithmetic progressions is one of the great triumphs of the "Hung...

szemeredi

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Ke Gong

CS Theory @ Princeton : Additive Combinatorics Minicourse - 0 views

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    Additive Combinatorics and Computer Science
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AIM math: GL(3) Maass forms and L-functions - 0 views

  • wo researchers from the University of Bristol exhibited the first example of a third degree transcendental L-function.
  • "This work was made possible by a combination of theoretical advances and the power of modern computers." During his lecture, Bian reported that it took approximately 10,000 hours of computer time to produce his initial results.
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Neal Stephenson on Zeta Function Cryptography - 0 views

  • M. Anshel and D. Goldfeld, "Zeta Functions, One-Way Functions, and Pseudorandom Number Generators", Duke Mathematical Journal, Vol. 88 No. 2 (1997) 371-390. "In 1997,Anshel and Goldfeld [6],presented an explicit construction of a pseudorandom number generator arising from an elliptic curve,which can be effectively computed at low computational cost. They introduced a new intractable problem,distinct from integer factorization or the discrete log problem, that leads to a new class of one-way functions based on the theory of zeta functions,and against which there is no known attack."- Richard M. Mollin,"Introduction to Cryptography" CRC Press (2000)
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Mathematics of Computation - 0 views

  • We verify a very recent conjecture of Farmer and Rhoades on the asymptotic rate of growth of the derivatives of the Riemann xi function at . We give two separate proofs of this result, with the more general method not restricted to . We briefly describe other approaches to our results, give a heuristic argument, and mention supporting numerical evidence.
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Pseudorandom number generation by p-adic ergodic transformations. arXiv Mathematics - C... - 0 views

  • Abstract. The paper study counter-dependent pseudorandom number generators based on m-variate (m> 1) ergodic mappings of the space of 2-adic integers Z2. The sequence of internal states of these generators is defined by the recurrence law xi+1 = H B i (xi) mod 2 n, whereas their output sequence is zi = F B i (xi) mod 2 n; here xj, zj are m-dimensional vectors over Z2. It is shown how the results obtained for a univariate case could be extended to a multivariate case. 1.
  • Foundations of Cryptography. Basic Tools. Cambridge Univ – Goldreich - 2001
  • 129 Uniform distribution of sequences – Kuipers, Niederreiter - 1974
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  • 22 The art of computer programming. Vol. 2: Seminumerical Algorithms – Knuth - 1981
  • 8 Uniformly distributed sequences of p-adic integers – Anashin - 1994
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The Large Sieve and its Applications - Cambridge University Press - 0 views

  • Among the modern methods used to study prime numbers, the ‘sieve’ has been one of the most efficient. Originally conceived by Linnik in 1941, the ‘large sieve’ has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.• Explores new and surprising applications of the large sieve method, an important technique of analytic number theory • Presents applications in fields as wide ranging as topology, probability, arithmetic geometry and discrete group theory • Motivated, clear and self-contained discussions introduce readers to a technique previously confined to one fieldContentsPreface; Prerequisites and notation; 1. Introduction; 2. The principle of the large sieve; 3. Group and conjugacy sieves; 4. Elementary and classical examples; 5. Degrees of representations of finite groups; 6. Probabilistic sieves; 7. Sieving in discrete groups; 8. Sieving for Frobenius over finite fields; Appendix A. Small sieves; Appendix B. Local density computations over finite fields; Appendix C. Representation theory; Appendix D. Property (T) and Property (τ); Appendix E. Linear algebraic groups; Appendix F. Probability theory and random walks; Appendix G. Sums of multiplicative functions; Appendix H. Topology; Bibliography; Index.
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The Möbius and nilsequences conjecture « What's new - 0 views

  • There is an amusing way to interpret the conjecture (using the close relationship between nilsequences and bracket polynomials) as an assertion of the pseudorandomness of the Liouville function from a computational complexity perspective.   
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Structure and randomness in combinatorics « What's new - 0 views

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    I've just uploaded to the arXiv my lecture notes "Structure and randomness in combinatorics" for my tutorial at the upcoming FOCS 2007 conference in October. This tutorial covers similar ground as my ICM paper (or slides), or my first two Simons lectures, but focuses more on the "nuts-and-bolts" of how structure theorems actually work to separate objects into structured pieces and pseudorandom pieces, for various definitions of "structured" and "pseudorandom".  Given that the target audience consists of computer scientists, I have focused exclusively here on the combinatorial aspects of this dichotomy (applied for instance to functions on the Hamming cube) rather than, say, the ergodic theory aspects (which are covered in Bryna Kra's lecture notes from Montreal, or my notes from Montreal for that matter).  While most of the known applications of these decompositions are number-theoretic (e.g. my theorem with Ben Green), the number theory aspects are not covered in detail in these notes.  (For that, you can read Bernard Host's Bourbaki article, Ben Green's http
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Mathematics of Computation - 0 views

  • For any and any non-exceptional modulus , we prove that, for large enough ( ), the interval contains a prime in any of the arithmetic progressions modulo . We apply this result to establish that every integer larger than is a sum of seven cubes.
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Recent Perspectives in Random Matrix Theory and Number Theory - Cambridge University Pr... - 0 views

  • In recent years the application of random matrix techniques to analytic number theory has been responsible for major advances in this area of mathematics. As a consequence it has created a new and rapidly developing area of research. The aim of this book is to provide the necessary grounding both in relevant aspects of number theory and techniques of random matrix theory, as well as to inform the reader of what progress has been made when these two apparently disparate subjects meet. This volume of proceedings is addressed to graduate students and other researchers in both pure mathematics and theoretical physics. The contributing authors, who are among the world leading experts in this area, have taken care to write self-contained lectures on subjects chosen to produce a coherent volume.• Self-contained lectures by world-leading experts in the field • The volume is integrated, indexed and cross-referenced • This title covers the most important and recent advances in the subjectContents1. Introduction; 2. Prime number theory and the Riemann zeta-function; 3. Notes on pair correlation of zeros and prime numbers; 4. Notes on eigenvalue distributions for the classical compact groups; 5. Compound nucleus resonances, random matrices and quantum chaos; 6. Families of L-functions and 1-level densities; 7. Basic analytic number theory; 8. Applications of mean value theorems to the theory of the Riemann zeta function; 9. L-functions and the characteristic polynomials of random matrices; 10. Mock gaussian behaviour; 11. Some specimens of L-functions; 12. Computational methods and experiments in analytic number theory.
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Science News Online: Ivars Peterson's MathTrek (6/26/99): The Return of Zeta - 0 views

  • References: Cipra, B. 1998. A prime case of chaos. In What's Happening in the Mathematical Sciences, Vol. 4. Providence, R.I.: American Mathematical Society. (Available at http://www.ams.org/new-in-math/happening.html.) ______. 1996. Prime formula weds number theory and quantum physics. Science 274(Dec. 20):2014. Davis, P.J., and R. Hersch. 1981. The Mathematical Experience. New York: Viking Penguin. Katz, N.M., and P. Sarnak. 1999. Zeroes of zeta functions and symmetry. Bulletin of the American Mathematical Society 36(January):1. Peterson, I. 1995. Cavities of chaos. Science News 147(April 29):264. Richards, I. 1978. Number theory. In Mathematics Today: Twelve Informal Essays. L.A. Steen, ed. New York: Springer-Verlag. Peter Sarnak's lecture on random matrix models in number theory and quantum mechanics is available at http://www.msri.org/publications/video/fall98/mandm.html. Andrew Odlyzko's Web page at http://www.research.att.com/~amo/ features computations of the zeros of the zeta function.
  • The Riemann hypothesis was first proposed in 1859 by the German mathematician Georg Friedrich Bernhard Riemann (1826-1866). It concerns the so-called zeta function, which encodes a great deal of information about the seemingly haphazard distribution of prime numbers among the integers (see The Mark of Zeta, June 19, 1999).
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