Relevant bibliographies by topics / Algebraic number theory

Academic literature on the topic 'Algebraic number theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 2 March 2023

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Journal articles on the topic "Algebraic number theory":

1

Blackmore, G. W., I. N. Stewart, and D. O. Tall. "Algebraic Number Theory." Mathematical Gazette 73, no. 463 (March 1989): 65. http://dx.doi.org/10.2307/3618234.

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S., R., and Michael E. Pohst. "Computational Algebraic Number Theory." Mathematics of Computation 64, no. 212 (October 1995): 1763. http://dx.doi.org/10.2307/2153389.

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Karve, Aneesh, and Sebastian Pauli. "GiANT: Graphical Algebraic Number Theory." Journal de Théorie des Nombres de Bordeaux 18, no. 3 (2006): 721–27. http://dx.doi.org/10.5802/jtnb.569.

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Lenstra Jr., H. W. "Algorithms in Algebraic Number Theory." Bulletin of the American Mathematical Society 26, no. 2 (October 1, 1992): 211–45. http://dx.doi.org/10.1090/s0273-0979-1992-00284-7.

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Platonov, V. P., and A. S. Rapinchuk. "Algebraic groups and number theory." Russian Mathematical Surveys 47, no. 2 (April 30, 1992): 133–61. http://dx.doi.org/10.1070/rm1992v047n02abeh000879.

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Appleby, Marcus, Steven Flammia, Gary McConnell, and Jon Yard. "SICs and Algebraic Number Theory." Foundations of Physics 47, no. 8 (April 24, 2017): 1042–59. http://dx.doi.org/10.1007/s10701-017-0090-7.

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Belabas, Karim. "Topics in computational algebraic number theory." Journal de Théorie des Nombres de Bordeaux 16, no. 1 (2004): 19–63. http://dx.doi.org/10.5802/jtnb.433.

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Schoof, Ren\'e. "Book Review: Algorithmic algebraic number theory." Bulletin of the American Mathematical Society 29, no. 1 (July 1, 1993): 111–14. http://dx.doi.org/10.1090/s0273-0979-1993-00392-6.

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Krishna, Amalendu, and Jinhyun Park. "Algebraic cobordism theory attached to algebraic equivalence." Journal of K-Theory 11, no. 1 (February 2013): 73–112. http://dx.doi.org/10.1017/is013001028jkt210.

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Abstract:
AbstractBased on the algebraic cobordism theory of Levine and Morel, we develop a theory of algebraic cobordism modulo algebraic equivalence.We prove that this theory can reproduce Chow groups modulo algebraic equivalence and the semi-topological K0-groups. We also show that with finite coefficients, this theory agrees with the algebraic cobordism theory.We compute our cobordism theory for some low dimensional varieties. The results on infinite generation of some Griffiths groups by Clemens and on smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in terms of this cobordism theory.
10

Cremona, J. E., and Henri Cohen. "A Course in Computational Algebraic Number Theory." Mathematical Gazette 78, no. 482 (July 1994): 221. http://dx.doi.org/10.2307/3618596.

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Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Algebraic number theory":

1

Röttger, Christian Gottfried Johannes. "Counting problems in algebraic number theory." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327407.

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Swanson, Colleen M. "Algebraic number fields and codes /." Connect to online version, 2006. http://ada.mtholyoke.edu/setr/websrc/pdfs/www/2006/172.pdf.

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Hughes, Garry. "Distribution of additive functions in algebraic number fields." Title page, contents and summary only, 1987. http://web4.library.adelaide.edu.au/theses/09SM/09smh893.pdf.

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McCoy, Daisy Cox. "Irreducible elements in algebraic number fields." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/39950.

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Gaertner, Nathaniel Allen. "Special Cases of Density Theorems in Algebraic Number Theory." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/33153.

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This paper discusses the concepts in algebraic and analytic number theory used in the proofs of Dirichlet's and Cheboterev's density theorems. It presents special cases of results due to the latter theorem for which greatly simplified proofs exist.
Master of Science
6

Rozario, Rebecca. "The Distribution of the Irreducibles in an Algebraic Number Field." Fogler Library, University of Maine, 2003. http://www.library.umaine.edu/theses/pdf/RozarioR2003.pdf.

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Nyqvist, Robert. "Algebraic Dynamical Systems, Analytical Results and Numerical Simulations." Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1142.

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Yan, Song Yuan. "On the algebraic theories and computations of amicable numbers." Thesis, University of York, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284133.

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Haydon, James Henri. "Étale homotopy sections of algebraic varieties." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:88019ba2-a589-4179-ad7f-1eea234d284c.

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We define and study the fundamental pro-finite 2-groupoid of varieties X defined over a field k. This is a higher algebraic invariant of a scheme X, analogous to the higher fundamental path 2-groupoids as defined for topological spaces. This invariant is related to previously defined invariants, for example the absolute Galois group of a field, and Grothendieck’s étale fundamental group. The special case of Brauer-Severi varieties is considered, in which case a “sections conjecture” type theorem is proved. It is shown that a Brauer-Severi variety X has a rational point if and only if its étale fundamental 2-groupoid has a special sort of section.
10

Green, Benjamin. "Galois representations attached to algebraic automorphic representations." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:77f01cbc-65d1-480d-ae3a-0a039a76671a.

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This thesis is concerned with the Langlands program; namely the global Langlands correspondence, Langlands functoriality, and a conjecture of Gross. In chapter 1, we cover the most important background material needed for this thesis. This includes material on reductive groups and their root data, the definition of automorphic representations and a general overview of the Langlands program, and Gross' conjecture concerning attaching l-adic Galois representations to automorphic representations on certain reductive groups G over ℚ. In chapter 2, we show that odd-dimensional definite unitary groups satisfy the hypotheses of Gross' conjecture and verify the conjecture in this case using known constructions of automorphic l-adic Galois representations. We do this by verifying a specific case of a generalisation of Gross' conjecture; one should still get l-adic Galois representations if one removes one of his hypotheses but with the cost that their image lies in CG(ℚl) as opposed to LG(ℚl). Such Galois representations have been constructed for certain automorphic representations on G, a definite unitary group of arbitrary dimension, and there is a map CG(ℚl) → LG(ℚl) precisely when G is odd-dimensional. In chapter 3, which forms the main part of this thesis, we show that G = Un(B) where B is a rational definite quaternion algebra satisfies the hypotheses of Gross' conjecture. We prove that one can transfer a cuspidal automorphic representation π of G to a π' on Sp2n (a Jacquet-Langlands type transfer) provided it is Steinberg at some finite place. We also prove this when B is indefinite. One can then transfer π′ to an automorphic representaion of GL2n+1 using the work of Arthur. Finally, one can attach l-adic Galois representations to these automorphic representations on GL2n+1, provided we assume π is regular algebraic if B is indefinite, and show that they have orthogonal image.
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Books on the topic "Algebraic number theory":

1

Weiss, Edwin. Algebraic number theory. Mineola, N.Y: Dover Publications, 1998.

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Fröhlich, A. Algebraic number theory. Cambridge: Cambridge University Press, 1991.

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Lang, Serge. Algebraic number theory. 2nd ed. New York: Springer-Verlag, 1994.

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Koch, H. Algebraic Number Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-58095-6.

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Lang, Serge. Algebraic Number Theory. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4684-0296-4.

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Neukirch, Jürgen. Algebraic Number Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03983-0.

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Jarvis, Frazer. Algebraic Number Theory. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07545-7.

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Lang, Serge. Algebraic Number Theory. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0853-2.

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Orme, Tall David, ed. Algebraic number theory. 2nd ed. London: Chapman and Hall, 1987.

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Mollin, Richard A. Algebraic number theory. 2nd ed. Boca Raton, FL: Chapman and Hall/CRC, 2011.

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Book chapters on the topic "Algebraic number theory":

1

Geroldinger, Alfred. "Factorizations of algebraic integers." In Number Theory, 63–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0086545.

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Ireland, Kenneth, and Michael Rosen. "Algebraic Number Theory." In A Classical Introduction to Modern Number Theory, 172–87. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4757-2103-4_12.

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Stillwell, John. "Algebraic Number Theory." In Undergraduate Texts in Mathematics, 404–30. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4684-9281-1_21.

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Stillwell, John. "Algebraic Number Theory." In Undergraduate Texts in Mathematics, 439–66. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6053-5_21.

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Weil, André. "Algebraic number-fields." In Basic Number Theory, 80–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-61945-8_5.

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Kolmogorov, A. N., and A. P. Yushkevich. "Algebra and Algebraic Number Theory." In Mathematics of the 19th Century, 35–135. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8293-4_2.

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Bashmakova, I. G., and A. N. Rudakov. "Algebra and Algebraic Number Theory." In Mathematics of the 19th Century, 35–135. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-5112-1_2.

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Bourbaki, Nicolas. "Commutative Algebra. Algebraic Number Theory." In Elements of the History of Mathematics, 93–115. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-61693-8_7.

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Fine, Benjamin, and Gerhard Rosenberger. "Primes and Algebraic Number Theory." In Number Theory, 285–370. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43875-7_6.

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Koch, H. "Basic Number Theory." In Algebraic Number Theory, 8–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-58095-6_1.

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Conference papers on the topic "Algebraic number theory":

1

Lam, S. P., and K. P. Shum. "Algebraic Structures and Number Theory." In First International Symposium on Algebraic Structures and Number Theory. WORLD SCIENTIFIC, 1990. http://dx.doi.org/10.1142/9789814540209.

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Huang, Yu-Chih. "Lattice index codes from algebraic number fields." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282903.

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van Dam, Wim, and Yoshitaka Sasaki. "QUANTUM ALGORITHMS FOR PROBLEMS IN NUMBER THEORY, ALGEBRAIC GEOMETRY, AND GROUP THEORY." In Summer School on Diversities in Quantum Computation/Information. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814425988_0003.

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Tsuboi, Shoji. "The Euler number of the normalization of an algebraic threefold with ordinary singularities." In Geometric Singularity Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2004. http://dx.doi.org/10.4064/bc65-0-17.

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Feng, Ke-Qin, and Ke-Zheng Li. "Proceedings of the Special Program at Nankai Institute of Mathematics ALGEBRAIC GEOMETRY and ALGEBRAIC NUMBER THEORY." In Special Program at Nankai Institute of Mathematics. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814537681.

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Limniotis, Konstantinos, Nicholas Kolokotronis, and Nicholas Kalouptsidis. "Constructing Boolean functions in odd number of variables with maximum algebraic immunity." In 2011 IEEE International Symposium on Information Theory - ISIT. IEEE, 2011. http://dx.doi.org/10.1109/isit.2011.6034059.

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Xiaowen Xiong, Xia Yang, and Chi Ma. "Analysis of the number of even-variable boolean functions with maximum algebraic immunity." In Symposium on ICT and Energy Efficiency and Workshop on Information Theory and Security (CIICT 2012). Institution of Engineering and Technology, 2012. http://dx.doi.org/10.1049/cp.2012.1869.

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Alekseev, Yaroslav, Dima Grigoriev, Edward A. Hirsch, and Iddo Tzameret. "Semi-algebraic proofs, IPS lower bounds, and the τ-conjecture: can a natural number be negative?" In STOC '20: 52nd Annual ACM SIGACT Symposium on Theory of Computing. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3357713.3384245.

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Martino, Anthony J., and G. Michael Morris. "Optical generation of random numbers: theory and experiments." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.tue2.

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Simulation of physical processes and Monte Carlo solutions to numerical problems on digital computers require sources of random numbers that follow specified density functions. In our experiments, the spatial coordinates of detected photoevents are used as a fast source of true random numbers to solve numerical problems by the Monte Carlo method. The probability density function for the location of a photoevent on the detector surface is proportional to the irradiance. We have constructed an optical random number generator using a microchannel plate detector with a resistive anode. It can produce bivariate random deviates with any probability density and any correlation between the two variables. The numbers pass the standard tests for randomness and fit to the given distributions (chi-square, correlation, sequence tests). Nonuniform distributions can be obtained with no loss of speed by manipulating the irradiance distribution across the detector, e.g., by imaging a transparency onto it. In particular, we have produced uniformly distributed random numbers and normally distributed random numbers with various correlations between the variables. We have also used the optical random number generator to find approximate solutions to systems of large linear algebraic equations and approximations to the inverses of large matrices, with a maximum error of <5%.
10

Sheppard, S. D., D. J. Wilde, and Y. L. Hsu. "Algebraic Acceleration of Finite Element Optimization; Four Modeling Errors in a Weldment Design." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0063.

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Abstract A method is proposed for incorporating finite element stress analysis into the constraints of an optimization model. To reduce the number of computationally intensive finite element analyses, the more accurate FEA plate model is approximated by an algebraic beam model having an adjustable factor whose value is determined by comparing FEA stresses with the corresponding beam theory predictions. This factor compensates both for the inaccuracies of beam theory and the effect of stress concentration. The algebraic form is retained to permit application of powerful optimization techniques not applicable directly to finite element models. The optimization problem is thus reduced to the determination of the single factor by linear interpolation. When tested on Keith’s well-known welded cantilever problem, the method needs only three FEAs. Keith’s model is also shown to suffer from four errors, of which three are remedied here. Because of special problem structure, the resulting design is correct for three of the four design variables, but the length of the weld cannot be determined without a better weld stress model.

Reports on the topic "Algebraic number theory":

1

Xia, Xiang-Gen. Space-Time Coding Using Algebraic Number Theory for Broadband Wireless Communications. Fort Belvoir, VA: Defense Technical Information Center, May 2008. http://dx.doi.org/10.21236/ada483791.

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Sultanov, S. R. Electronic textbook " Algebra and number theory. Part 2 "direction of training 02.03.03" Mathematical support and administration of information systems". OFERNIO, June 2018. http://dx.doi.org/10.12731/ofernio.2018.23685.

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