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Relevant bibliographies by topics / Theory of quadratic forms

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Academic literature on the topic 'Theory of quadratic forms'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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Journal articles on the topic "Theory of quadratic forms"

1

Sigrist, François. "Cyclotomic quadratic forms." Journal de Théorie des Nombres de Bordeaux 12, no. 2 (2000): 519–30. http://dx.doi.org/10.5802/jtnb.295.

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Alpers, Burkhard. "Round quadratic forms." Journal of Algebra 137, no. 1 (1991): 44–55. http://dx.doi.org/10.1016/0021-8693(91)90080-r.

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Alpers, Burkhard. "Semiround Quadratic Forms." Communications in Algebra 18, no. 3 (1990): 741–53. http://dx.doi.org/10.1080/00927879008823941.

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Hornix, E. A. M. "Round Quadratic Forms." Journal of Algebra 175, no. 3 (1995): 820–43. http://dx.doi.org/10.1006/jabr.1995.1216.

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Solov'ev, Yu P. "Algebraic K-theory of quadratic forms." Journal of Soviet Mathematics 44, no. 3 (1989): 319–71. http://dx.doi.org/10.1007/bf01676869.

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Alaca, Ayşe, Şaban Alaca, Mathieu F. Lemire, and Kenneth S. Williams. "Nineteen quaternary quadratic forms." Acta Arithmetica 130, no. 3 (2007): 277–310. http://dx.doi.org/10.4064/aa130-3-5.

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Alaca, Ayşe, Şaban Alaca, and Kenneth S. Williams. "Seven octonary quadratic forms." Acta Arithmetica 135, no. 4 (2008): 339–50. http://dx.doi.org/10.4064/aa135-4-3.

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Duke, W. "On ternary quadratic forms." Journal of Number Theory 110, no. 1 (2005): 37–43. http://dx.doi.org/10.1016/j.jnt.2004.06.013.

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ALACA, AYŞE, ŞABAN ALACA, and KENNETH S. WILLIAMS. "FOURTEEN OCTONARY QUADRATIC FORMS." International Journal of Number Theory 06, no. 01 (2010): 37–50. http://dx.doi.org/10.1142/s179304211000279x.

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We use the recent evaluation of certain convolution sums involving the sum of divisors function to determine the number of representations of a positive integer by certain diagonal octonary quadratic forms whose coefficients are 1, 2 or 4.

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Car, Mireille. "Quadratic Forms onFq[T]." Journal of Number Theory 61, no. 1 (1996): 145–80. http://dx.doi.org/10.1006/jnth.1996.0142.

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Dissertations / Theses on the topic "Theory of quadratic forms"

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McQuillan, Daniel J. "Quadratic forms and Galois theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0013/NQ31148.pdf.

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Shao, You Yu. "Representation theory of quadratic forms /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487858106116574.

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Shaughnessy, John F. "Finding Zeros of Rational Quadratic Forms." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/cmc_theses/849.

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In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.

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Liu, Dunxue Carleton University Dissertation Mathematics. "Dihedral polynomial congruences and binary quadratic forms: a class field theory approach." Ottawa, 1992.

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Meyer, Nicolas David. "Determination of Quadratic Lattices by Local Structure and Sublattices of Codimension One." OpenSIUC, 2015. https://opensiuc.lib.siu.edu/dissertations/1026.

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For definite quadratic lattices over the rings of integers of algebraic number fields, it is shown that lattices are determined up to isometry by their local structure and sublattices of codimension 1. In particular, a theorem of Yoshiyuki Kitaoka for $\mathbb{Z}$-lattices is generalized to definite lattices over algebraic number fields.

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Myerson, Simon L. Rydin. "Systems of forms in many variables." Thesis, University of Oxford, 2016. http://ora.ox.ac.uk/objects/uuid:a9932e90-4784-466a-a694-d387c1228533.

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We consider systems of polynomial equations and inequalities to be solved in integers. By applying the circle method, when the number of variables is large and the system is geometrically well-behaved we give an asymptotic estimate for the number of solutions of bounded size. In the case of R homogeneous equations having the same degree d, a classic theorem of Birch provides such an estimate provided the number of variables is R(R+1)(d-1)2<sup>d-1</sup>+R or greater and the system is nonsingular. In many cases this conclusion has been improved, but except in the case of diagonal equations the

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Constable, Jonathan A. "Kronecker's Theory of Binary Bilinear Forms with Applications to Representations of Integers as Sums of Three Squares." UKnowledge, 2016. http://uknowledge.uky.edu/math_etds/35.

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In 1883 Leopold Kronecker published a paper containing “a few explanatory remarks” to an earlier paper of his from 1866. His work loosely connected the theory of integral binary bilinear forms to the theory of integral binary quadratic forms. In this dissertation we discover the statements within Kronecker's paper and offer detailed arithmetic proofs. We begin by developing the theory of binary bilinear forms and their automorphs, providing a classification of integral binary bilinear forms up to equivalence, proper equivalence and complete equivalence. In the second chapter we introduce the c

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Gunawardana, Beruwalage Lakshika Kumari. "LOCALLY PRIMITIVELY UNIVERSAL FORMS AND THE PRIMITIVE COUNTERPART TO THE FIFTEEN THEOREM." OpenSIUC, 2020. https://opensiuc.lib.siu.edu/dissertations/1827.

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An n-dimensional integral quadratic form over Z is a polynomial of the form f = f(x1, … ,xn) =∑_(1≤i,j ≤n)▒a_ij x_i x_j, where a_ij=a_ji in Z. An integral quadratic form is called positive definite if f(α_1, …,α_n) > 0 whenever (0, … , 0) ≠(α_1, …,α_n) in Z^n. A positive definite integral quadratic form is said to be almost (primitively) universal if it (primitively) represents all but at most finitely many positive integers. In general, almost primitive universality is a stronger property than almost universality. Main results of this study are: every primitively universal form non-trivially

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Silva, Alexsandro BelÃm da. "FamÃlias infinitas de corpos quadrÃticos imaginÃrios." Universidade Federal do CearÃ, 2010. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5664.

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FundaÃÃo de Amparo Ã Pesquisa do Estado do CearÃ<br>CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>Seja ℓ > 3 um primo Ãmpar. Sejam So, S+, S_ conjuntos finitos mutuamente disjuntos de primos racionais. Para qualquer nÃmero real suficientemente grande X > 0, baseando-nos em [16], damos neste trabalho, um limite inferior do nÃmero de corpos quadrÃticos imaginÃrios k que satisfazem as seguintes condiÃÃes: o discriminante de k Ã maior que -X o nÃmero de classe de k Ã nÃo divisÃvel por ℓ, todo q â So se ramifica, todo q â S+ se decompÃe e todo q â S_ Ã inerte em k, resp

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Matos, Fábio Alexandre de 1976. "Teorema 90 de Hilbert para o radical de Kaplansky e suas relações com o grupo de Galois do fecho quadrático." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306552.

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Orientador: Antonio José Engler<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-24T22:18:49Z (GMT). No. of bitstreams: 1 Matos_FabioAlexandrede_D.pdf: 1117786 bytes, checksum: ce8cedb8cf95de8f81d4d520e2d308ad (MD5) Previous issue date: 2014<br>Resumo: Apresentaremos neste trabalho um estudo sobre a aritmética corpos de característica distinta de 2 com um número finito de classes de quadrados. Dividido em duas partes, começaremos com um estudo do radical de Kaplansky de um corpo F e se

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Books on the topic "Theory of quadratic forms"

1

Koshmanenko, Volodymyr. Singular Quadratic Forms in Perturbation Theory. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4619-7.

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Koshmanenko, V. D. Singular quadratic forms in perturbation theory. Kluwer, 1999.

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Koshmanenko, Volodymyr. Singular Quadratic Forms in Perturbation Theory. Springer Netherlands, 1999.

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Mathai, A. M. Quadratic forms in random variables: Theory and applications. M. Dekker, 1992.

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Ranicki, Andrew. Algebraic L̲-theory and topological manifolds. Cambridge University Press, 1992.

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Jardine, J. F. Higher spinor classes. American Mathematical Society, 1994.

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Baeza, Ricardo, John S. Hsia, Bill Jacob, and Alexander Prestel, eds. Algebraic and Arithmetic Theory of Quadratic Forms. American Mathematical Society, 2004. http://dx.doi.org/10.1090/conm/344.

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Marshall, Murray A. Spaces of orderings and abstract real spectra. Springer, 1996.

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Buell, Duncan A. Binary quadratic forms: Classical theory and modern computations. Springer-Verlag, 1989.

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1966-, Karpenko Nikita, and Merkurjev Alexander 1955-, eds. The algebraic and geometric theory of quadratic forms. American Mathematical Society, 2008.

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Book chapters on the topic "Theory of quadratic forms"

1

Trifković, Mak. "Quadratic Forms." In Algebraic Theory of Quadratic Numbers. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7717-4_7.

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Chevalley, Claude. "Quadratic Forms." In The Algebraic Theory of Spinors and Clifford Algebras. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60934-3_5.

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Ortega, James M. "Quadratic Forms and Optimization." In Matrix Theory. Springer US, 1987. http://dx.doi.org/10.1007/978-1-4899-0471-3_4.

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O’Meara, O. Timothy. "Dedekind Theory of Ideals." In Introduction to Quadratic Forms. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-62031-7_2.

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O’Meara, O. Timothy. "Fields of Number Theory." In Introduction to Quadratic Forms. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-62031-7_3.

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Koshmanenko, Volodymyr. "Singular Quadratic Forms." In Singular Quadratic Forms in Perturbation Theory. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4619-7_3.

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Coppel, W. A. "The Arithmetic of Quadratic Forms." In Number Theory. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-89486-7_7.

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O’Meara, O. Timothy. "Integral Theory of Quadratic Forms over Global Fields." In Introduction to Quadratic Forms. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-62031-7_10.

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O’Meara, O. Timothy. "Integral Theory of Quadratic Forms over Local Fields." In Introduction to Quadratic Forms. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-62031-7_9.

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Sambale, Benjamin. "Quadratic Forms." In Blocks of Finite Groups and Their Invariants. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12006-5_3.

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Conference papers on the topic "Theory of quadratic forms"

1

Courtright, Logan, Pradyoth Shandilya, Thomas F. Carruthers, and Curtis R. Menyuk. "Formation of Multiple Stable Regions for Single Solitons in the Presence of an Avoided Crossing." In Frontiers in Optics. Optica Publishing Group, 2024. https://doi.org/10.1364/fio.2024.jtu4a.14.

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Standard soliton theory for quadratic dispersion microresonators predicts an infinitely large region for soliton stability past α=3. In the presence of an avoided crossing, we show that multiple isolated regions of stability can form.

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Shen, Kaiming, Ziping Zhao, Yannan Chen, Zepeng Zhang, and Hei Victor Cheng. "Accelerating Quadratic Transform and WMMSE." In 2024 IEEE International Symposium on Information Theory (ISIT). IEEE, 2024. http://dx.doi.org/10.1109/isit57864.2024.10619169.

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Schmidt, Kai-Uwe. "ℤ4-valued quadratic forms and exponential sums." In 2008 IEEE International Symposium on Information Theory - ISIT. IEEE, 2008. http://dx.doi.org/10.1109/isit.2008.4595495.

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Wu, Baofeng. "New classes of quadratic bent functions in polynomial forms." In 2014 IEEE International Symposium on Information Theory (ISIT). IEEE, 2014. http://dx.doi.org/10.1109/isit.2014.6875150.

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Chen, Wenbing, Jinquan Luo, and Yuansheng Tang. "Exponential sum from half quadratic forms and its application." In 2014 IEEE International Symposium on Information Theory (ISIT). IEEE, 2014. http://dx.doi.org/10.1109/isit.2014.6875414.

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Pitaval, Renaud-Alexandre, and Yi Qin. "Grassmannian Frames in Composite Dimensions by Exponentiating Quadratic Forms." In 2020 IEEE International Symposium on Information Theory (ISIT). IEEE, 2020. http://dx.doi.org/10.1109/isit44484.2020.9174082.

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Tekcan, Ahmet, Arzu Özkoç, Ismail Naci Cangül, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Indefinite Quadratic Forms and their Neighbours." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3497837.

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Al-Naffouri, Tareq Y., and Babak Hassibi. "On the distribution of indefinite quadratic forms in Gaussian random variables." In 2009 IEEE International Symposium on Information Theory - ISIT. IEEE, 2009. http://dx.doi.org/10.1109/isit.2009.5205261.

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McKay, Matthew, Peter Smith, and Iain Collings. "New Properties of Complex Noncentral Quadratic Forms and Bounds on MIMO Mutual Information." In 2006 IEEE International Symposium on Information Theory. IEEE, 2006. http://dx.doi.org/10.1109/isit.2006.261997.

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Karystinos, George N., and Athanasios P. Liavas. "Quadratic form maximization over the binary field with polynomial complexity." In 2008 IEEE International Symposium on Information Theory - ISIT. IEEE, 2008. http://dx.doi.org/10.1109/isit.2008.4595431.

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Reports on the topic "Theory of quadratic forms"

1

Bock, Mary E., and Herbert Solomon. Distributions of Quadratic Forms. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada190224.

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McMath, Stephen S. Parallel Integer Factorization Using Quadratic Forms. Defense Technical Information Center, 2005. http://dx.doi.org/10.21236/ada436652.

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Maddocks, J. H. Restricted Quadratic Forms, Inertia Theorems and the Schur Complement,. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada185765.

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Yoshioka, Akira. Path Integral for Star Exponential Functions of Quadratic Forms. GIQ, 2012. http://dx.doi.org/10.7546/giq-4-2003-330-340.

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Hillier, Grant, Raymond Kan, and Xiaolu Wang. Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors. Institute for Fiscal Studies, 2008. http://dx.doi.org/10.1920/wp.cem.2008.1408.

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Heckman, James, Anne Layne-Farrar, and Petra Todd. The Schooling Quality-Earnings Relationship: Using Economic Theory to Interpret Functional Forms Consistent with the Evidence. National Bureau of Economic Research, 1995. http://dx.doi.org/10.3386/w5288.

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Nuttal, Albert H. Saddlepoint Approximation and First-Order Correction Term to the Joint Probability Density Function of M Quadratic and Linear Forms in K Gaussian Random Variables With Arbitrary Means and Covariances. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada389100.

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Liu, Xiang-Yang, Christopher D. Taylor, Eunja Kim, George Scott Goff, and David Gary Kolman. Corrosion mechanisms for metal alloy waste forms: experiment and theory Level 4 Milestone M4FT-14LA0804024 Fuel Cycle Research & Development. Office of Scientific and Technical Information (OSTI), 2014. http://dx.doi.org/10.2172/1148938.

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Apgar, Marina, Mieke Snijder, Pedro Prieto Martin, et al. Designing Contribution Analysis of Participatory Programming to Tackle the Worst Forms of Child Labour. Institute of Development Studies, 2022. http://dx.doi.org/10.19088/clarissa.2022.003.

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This Research and Evidence Paper presents the theory-based and participatory evaluation design of the Child Labour: Action-Research- Innovation in South and South-Eastern Asia (CLARISSA) programme. The evaluation is embedded in emergent Participatory Action Research with children and other stakeholders to address the drivers of the worst forms of child labour (WFCL). The report describes the use of contribution analysis as an overarching approach, with its emphasis on crafting, nesting and iteratively reflecting on causal theories of change. It illustrates how hierarchically-nested impact path

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Michalopoulos, C. D. PR-175-420-R01 Submarine Pipeline Analysis - Theoretical Manual. Pipeline Research Council International, Inc. (PRCI), 1985. http://dx.doi.org/10.55274/r0012171.

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Describes the computer program SPAN which computes the nonlinear transient response of a submarine pipeline, in contact with the ocean floor, to wave and current excitation. The dynamic response of a pipeline to impact loads, such as loads from trawl gear of fishing vessels, may also be computed. In addition, thermal expansion problems for submarine pipelines may be solved using SPAN. Beam finite element theory is used for spatial discretization of the partial differential equations governing the motion of a submarine pipeline. Large-deflection, small-strain theory is employed. The formulation

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