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Number theory (book list)

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This is a section of the Basic Math Library List. Please help to improve the article.


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The subject description:

3. Number theory
   Analytic and algebraic number theory. Local and global fields and their Galois groups. Zeta and L-functions. 
   Diophantine equations. Arithmetic on algebraic varieties. Diophantine approximation, transcendental number theory
   and geometry of numbers. Modular and automorphic forms, modular curves and Shimura varieties. Langlands program. 
   p-adic analysis. Number theory and physics. Computational number theory and applications, notably to cryptography.
   Connections with sections 1, 2, 4, 7, 12, 14, 15.


Number Theory: Introductory Texts

  • Andrews, George E. Number Theory. Dover Publications, 1998. ISBN 0486682528
    • Baker, Alan. A Concise Introduction to the Theory of Numbers New York, NY: Cambridge University Press, 1985. ISBN 0521286549.

Burn, R.P. A Pathway Into Number Theory New York, NY: Cambridge University Press, 1996. ISBN 0521575400

Burton, David M. Elementary Number Theory,New York, McGraw-Hill Companies, 1997. Second Edition. ISBN 0070094667

  • Davenport, Harold. The Higher Arithmetic: An Introduction to the Theory of Numbers, New York, NY: Cambridge University Press, 1998. ISBN 0521634466.
  • * Dence, Joseph B. & Thomas P. Elements of the Theory of Numbers. San Diego, Academic Press, 1999. ISBN 0122091302

Dudley, Underwood. Elementary Number Theory, New York, NY: W.H. Freeman, 1978. ISBN 071670076X.

Flath, Daniel E. Introduction to Number Theory New York, NY: John Wiley & Sons, Inc. 1989. ISBN 047160836X

  • * * Hardy, Godfrey H. and Wright, E. M. Introduction to the Theory of Numbers. Oxford University Press, 1980. ISBN 0198531702 (Out of Print)

Hua, Loo-Keng. Introduction to Number Theory. Springer- Verlag New York, 1987. ISBN 0387108181

Hurwitz, Adolf and Kritikos, Nikolaos. Lectures on Number Theory. Springer-Verlag New York, 1985 ISBN 0387962360

Kumanduri, Ramanujachary & Romero, Christina. Number Theory with Computer Applications. Paramus, Prentice Hall, 1997. ISBN 013801812X

Manin, Yuri and Panchishkin, A. A. Number Theory: Introduction to Number Theory. Encyclopaedia of Mathematical Sciences, Vol. 49, Parshin, A.N. and Shafarevich. I. R. eds. Berlin, Heidelberg, Springer-Verlag,1995. ISBN 3540533842

Mathews, George B. Theory of Numbers. Jamaica, Chelsea Publishing Company, (no date). ISBN 082840156X

  • Nagell, Trygve. Introduction to Number Theory Jamaica, Chelsea Publishing Company, 1981. ISBN 0828401632
      • Niven, Ivan M.; Zuckerman, Herbert S.; and Montgomery, Hugh L. An Introduction to the Theory of Numbers, New York, NY: John Wiley & Sons, 1991. ISBN 0471625469.

Rose, H.E. A Course in Number Theory Oxford University Press, 1995. ISBN 0198523769.

Rosen, Kenneth H. Elementary Number Theory and Its Applications, Addison Wesley Longman, Inc., 1992. ISBN 0201578891.

Shapiro, Harold N. Introduction to the Theory of Numbers New York, NY: John Wiley & Sons, 1983. ISBN 0471867373.

  • Stark, Harold M. An Introduction to Number Theory Reprint. MIT Press, 1978. ISBN 0262690608.
      • Weil, Andre. Number Theory for Beginners New York, NY: Springer-Verlag, 1985. ISBN 038790381X.


Number Theory: Expositions

  • Goldman, Jay. The Queen of Mathematics: A Historically Motivated Guide to Number Theory. Wellesley, MA, A.K. Peters, 1998. ISBN 1568810067
  • Khinchin, A. Ya. Three Pearls of Number Theory Bethesda, MD: Graylock Press, 1952. ISBN 0910670048.

Niven, Ivan M. Numbers: Rational and Irrational Washington, DC: Mathematical Association of America, 1961. ISBN 0883856018.

Niven, Ivan M. Irrational Numbers Washington, DC: Mathematical Association of America, 1956. ISBN 0883850117.

Ogilvy, C. Stanley and Anderson, John T. Excursions in Number Theory New York, NY: Dover Publications, Inc., 1988. ISBN 0486257789.

Ore, Oystein. Invitation to Number Theory Washington, DC: Mathematical Association of America, 1967. ISBN 0883856204.

  • * * Rademacher, Hans. Lectures on Elementary Number Theory. Reprint, Melbourne, Krieger Publishing Company, 1977. ISBN 0882754998
  • Scharlau, Winfried and Opolka, Hans. From Fermat to Minkowski: Lectures on the Theory of Numbers and Its Historical Development New York, NY: Springer-Verlag, 1984. ISBN 0387909427.
  • Schroeder, Manfred R. Number Theory in Science and Communication. New York, Springer-Verlag New York, 1991. ISBN 0387158006


Number Theory: Elementary Monographs

Davis, Philip J. The Lore of Large Numbers. Washington, Mathematical Association of America, 1961. ISBN 0883856069

Erdös, Paul and Graham, Ronald. Old and New Problems and Results in Combinatorial Number Theory. Springer-Verlag New York, 1998. ISBN 0387984607

  • Guy, Richard K. Unsolved Problems in Number Theory. Springer-Verlag New York, 1995. ISBN 0387942890

Khinchin, Aleksandr A. Continued Fractions. Reprint, Dover Publications, 1987. ISBN 0486696308

McCarthy, Paul J. Introduction to Arithmetical Functions. Springer-Verlag New York, 1985. ISBN 038796262X

Olds, Carl D. Continued Fractions. Washington, Mathematical Association of America, 1963. ISBN 0883856093

  • Ore, Oystein. Number Theory and Its History. Reprint, Dover Publications, 1988. ISBN 0486656209

Ribenboim, Paulo. 13 Lectures on Fermat's Last Theorem. Springer-Verlag New York, 1995. ISBN 0387904328

  • Shanks, Daniel. Solved and Unsolved Problems in Number Theory. Jamaica, Chelsea Publishing Company, 1985. ISBN 0828412979
  • Sierpinski, W. Elementary Theory of Numbers. New York, Elsevier Science, 1988. ISBN 0444866620

Sivaramakrishnan, R. Classical Theory of Arithmetic Functions. New York, M. Dekker, 1988. ISBN 0824780817

  • * * Van Der Poorten, A. J. Notes on Fermat's Last Theorem. New York, John Wiley, 1996. ISBN 0471062618


Primes and Factors

  • * * Bressoud, David M. Factorization and Primality Testing. Springer-Verlag New York, 1997. ISBN 0387970401

Brillhart, John et al. Factorizations of bn+1, b = 2,3,5,6,7, 10,11,12 up to High Powers. Providence, American Mathematical Society, 1988. ISBN 0821850784

Giblin, Peter. Primes and Programming, an Introduction to Number Theory with Computing. New York, Cambridge University Press, 1993. ISBN 0521409888

  • Ribenboim, Paulo. The Little Book of Big Primes. Springer- Verlag New York, 1993. ISBN 038797508X
  • Ribenboim, Paulo. The Book of Prime Number Records. Springer- Verlag New York, 1989. ISBN 0387970428

Riesel, Hans. Prime Numbers and Computer Methods for Factorization. Cambridge, Birkhauser Boston, 1994. ISBN 0817637435


Algebraic Number Theory

  • * * Borevich, Z.I. and Shafarevich, Igor R. Number Theory. Academic Press, 1986. ISBN 012117851X (Out of Print)

Buell, Duncan A. Binary Quadratic Forms. Springer-Verlag New York, 1989. ISBN 0387970371

+* Cohen, Henri. A Course in Computational Algebraic Number Theory. Berlin, New York, Springer-Verlag, 1993. ISBN 0387556400

  • Cohn, Harvey (Haim). A Classical Invitation to Algebraic Numbers and Class Fields. Springer-Verlag New York, 1995. ISBN 0387903453

Cox, David A. Primes of the Form x2 + ny2: Fermat, Class Field Theory, and Complex Multiplication. New York, John Wiley, 1997. ISBN 0471190799

Edwards, Harold M. Divisor Theory. Cambridge, Birkhauser Boston, 1989. ISBN 0817634487

Edwards, Harold M. Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory. Springer-Verlag New York, 1996. ISBN 0387902309

  • * * Ireland, Kenneth and Rosen, Michael I. A Classical Introduction to Modern Number Theory. Springer-Verlag New York, 1995. ISBN 038797329X

Janusz, Gerald J. Algebraic Number Fields. Providence, American Mathematical Society, 1995. ISBN 0821804294

+Lang, Serge. Algebraic Number Theory. Springer-Verlag New York, 1996. ISBN 0387942254

Marcus, Daniel A. Number Fields. Springer-Verlag New York, 1997. ISBN 0387902791

Milnor, John W. and Husemoller, D. Symmetric Bilinear Forms. Berlin, New York, Springer-Verlag, 1973. ISBN 038706009X (Out of Print)

  • * * Mollin, Richard A. Algebraic Number Theory. Boca Raton, London, New York, Washington, D.C., Chapman & Hall/CRC, 1999. ISBN 0849339898

Pohst, Michael and Zassenshaus, H. Algorithmic Algebraic Number Theory. New York, Cambridge University Press, 1997. ISBN 0521596696

  • Pollard, Harry and Diamond, Harold G. The Theory of Algebraic Numbers. Dover Publications, 1998. ISBN 0486404544

+* * * Serre, Jean-Pierre. A Course in Arithmetic. Springer- Verlag New York, 1996. ISBN 0387900403

+Silverman, Joseph H. and Tate, John. Rationial Points on Elliptic Curves. Springer-Verlag New York, 1992. ISBN 0387978259

+* Washington, Lawrence E. Introduction to Cyclotomic Fields. Springer-Verlag New York, 1996. ISBN 0387947620

+* Weil, Andre. Basic Number Theory. Springer-Verlag New York, 1995. ISBN 3540586555


Analytic Number Theory

+* * * Apostol, Tom M. Introduction to Analytic Number Theory. Springer-Verlag New York, 1995. ISBN 0387901639

  • * * Ayoub, Raymond. An Introduction to the Analytic Theory of Numbers. Ann Arbor, Books on Demand, (no date). ISBN 0608116270
  • * * Borwein, Jonathan M. and Borwein, Peter B. Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity. Vol 1, John Wiley, 1987 ISBN 047131515X

Chandrasekharan, Komaravolu. Introduction to Analytic Number Theory. Springer-Verlag New York, 1969. ISBN 0387041419

+* Davenport, Harold M. Multiplicative Number Theory. Springer-Verlag New York, 1980. ISBN 0387905332

Ellison, William J. and Ellison, Fern. Prime Numbers. New York, John Wiley, 1985. ISBN 0471826537

Graham, Sidney and Kolesnik, G. Van der Corput's Method for Exponential Sums. New York, Cambridge University Press, 1991. ISBN 0521339278

  • Grosswald, Emil. Representations of Integers as Sums of Squares. Springer-Verlag New York, 1985. ISBN 0387961267

Hooley, C. Applications of Sieve Methods to the Theory of Numbers. Cambridge, New York, Cambridge University Press, 1976. (Not in Books in Print)

  • Ingham, Albert E. The Distribution of Prime Numbers. New York, Cambridge University Press, 1990. ISBN 0521397898

Karatsuba, Anatolii Alekseevich. Basic Analytic Number Theory. Berlin, New York, Springer-Verlag, 1993. ISBN 0387533451

Karatsuba, Anatolii Alekseevich, and Voronin, S. M. The Riemann Zeta Function. Berlin, New York, Walter de Gruyter, 1992. ISBN 3110131706

Tenenbaum, Gerald. Introduction to Analytic and Probabilistic Number Theory. New York, Cambridge University Press, 1995. ISBN 0521412617

  • Vaughan, Robert C. The Hardy-Littlewood Method. New York, Cambridge University Press, 1997. ISBN 0521573475


Modular Forms

+* * Apostol, Tom. Modular Functions and Dirichlet Series in Number Theory. Spinger-Verlag New York, 1997. ISBN 0387971270

Chandrasekharan, Komaravolu. Elliptic Functions. Springer-Verlag New York, 1985. ISBN 0387152954

+Husemoller, Dale. Elliptic Curves. Springer-Verlag New York, 1997. ISBN 0387963715

+* * Knopp, Marvin I. Modular Functions in Analytic Number Theory. Chicago, Markham, 1970. ISBN 0828403376

+* * * Koblitz, Neal. Introduction to Elliptic Curves and Modular Forms. Springer-Verlag New York, 1996. ISBN 0387979662

+Lang, Serge. Elliptic Functions. Springer-Verlag New York, 1987. ISBN 0387965084

+Lang, Serge. Introduction to Modular Forms. Berlin, New York, Springer-Verlag, 1987. 0387078339

McKean Henry and Moll, V. Elliptic Curves, Function Theory, Geometry, Arithmetic. Cambridge, UK, New York, Cambridge University Press, 1999. 0521658179

+* Silverman, Joseph H. The Arithmetic of Elliptic Curves. Springer-Verlag New York, 1996. ISBN 0387962034

Weil, Andre. Elliptic Functions According to Eisenstein and Kronecker. Springer-Verlag New York, 1999. ISBN 3540650369


P-adic Fields

Fesenko, Ivan B. and Vostokov, S. Local Fields and their Extensions: A Constructive Approach. Providence, American Mathematical Society, 1993. ISBN 0821846132

+Koblitz, Neal. p-adic Numbers, p-adic Analysis, and Zeta Functions. Springer-Verlag New York, 1996. ISBN 0387960171

+* Koblitz, Neal. p-adic Analysis. New York, Cambridge University Press, 1980. ISBN 0521280605

+* Serre, Jean-Pierre. Local Fields. Springer-Verlag New York, 1995. ISBN 0387904247


Number Theory: Special Topics

  • Andrews, George E. The Theory of Partitions. New York, Cambridge University Press, 1998. ISBN 052163766X
  • Berndt, Bruce, Evans, R.J. and Williams, K. S. Gauss and Jacobi Sums. New York, Wiley, 1998. ISBN 0471128074

+Cassels, J.W. An Introduction to the Geometry of Numbers. Springer-Verlag New York, 1997. ISBN 3540617884

Ebbinghaus, Heinz-Dieter et al. Numbers. Springer-Verlag New York, 1990. ISBN 0387972021

Elliott, P.D.T.A. Probabilistic Number Theory, Central Limit Theorems. Springer-Verlag New York, 1980. ISBN 0387904387

  • * Fine, Nathan J. Basic Hypergeometric Series. Providence, American Mathematical Society, 1988. 0521350492
  • * Guy, R.K. Unsolved Problems in Number Theory. Springer-Verlag New York, 1995. 0387942890

King, R. Bruce. Beyond the Quartic Equation. Boston, Birkhauser, 1996. 0817637761

Lorentzen, Lisa and Waadeland, Haakon. Continued Fractions with Applications. Amsterdam, New York, North Holland, 1992. ISBN 0444892656

Parent, D.P. Exercises in Number Theory. Springer-Verlag New York, 1984. ISBN 0387960635

+ Ribenboim, Paulo. Catalan's Conjecture, are 8 and 9 the Only Consecutive Powers? Boston, Academic Press, 1994. ISBN 0125871708

  • Sierpinski, W.A. Problems in Elementary Number Theory. New York, Elsevier, 1980 ISBN 0444000712 (Out of Print)

+* Small, Charles. Arithmetic of Finite Fields. New York, M. Dekker, 1991. ISBN 0824785266

+ Wang, Yuan. Goldbach Conjecture. River Edge, World Scientific, 1984. ISBN 9971966085


Cryptography

+* Koblitz, Neal. A Course in Number Theory and Cryptography. Springer-Verlag New York, 1994. (Graduate Texts in Mathematics, 114.) ISBN 0387942939


Number Theory: History and Biography

Berndt, Bruce and Rankin, Robert A. Ramanujan: Letters and Commentary. Providence, American Mathematical Society, 1995. ISBN 0821802879

  • * Hoffman, Paul. The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth. Hyperion, 1999. ISBN 0786884061
  • Kanigel, Robert. The Man Who Knew Infinity. New York, Pocket Books, 1992. ISBN 0671750615 (Hardcover edition is "out of stock indefinitely.")
  • Schechter, Bruce. My Brain is Open: The Mathematical Journeys of Paul Erdös. New York, Simon & Schuster, 1998. ISBN 0684846357


Number Theory: Classic Works

  • Berndt, Bruce C. Ramanujan's Notebooks. Springer-Verlag New York, 1985-1998. 5 volumes.

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