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Journal articles on the topic 'Theory of quadratic forms'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Tammela, P. P. "Venkov's reduction theory of positive-quadratic forms." Journal of Soviet Mathematics 29, no. 3 (1985): 1306–12. http://dx.doi.org/10.1007/bf02108244.

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12

Koprowski, Przemysław. "Algorithms for quadratic forms." Journal of Symbolic Computation 43, no. 2 (2008): 140–52. http://dx.doi.org/10.1016/j.jsc.2007.10.004.

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13

Richter, Olav. "Theta functions of quadratic forms over imaginary quadratic fields." Acta Arithmetica 92, no. 1 (2000): 1–9. http://dx.doi.org/10.4064/aa-92-1-1-9.

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14

Kozioł, Krzysztof. "Quadratic forms over quadratic extensions of generalized local fields." Journal of Algebra 118, no. 1 (1988): 1–13. http://dx.doi.org/10.1016/0021-8693(88)90043-9.

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15

Nokhodkar, A. H. "Quadratic D-forms with applications to hermitian forms." Journal of Pure and Applied Algebra 224, no. 6 (2020): 106259. http://dx.doi.org/10.1016/j.jpaa.2019.106259.

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16

Car, Mireille. "Quadratic forms with polynomial coefficients." Acta Arithmetica 113, no. 2 (2004): 131–55. http://dx.doi.org/10.4064/aa113-2-2.

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17

Uludağ, A. Muhammed, Ayberk Zeytin, and Merve Durmuş. "Binary quadratic forms as dessins." Journal de Théorie des Nombres de Bordeaux 29, no. 2 (2017): 445–69. http://dx.doi.org/10.5802/jtnb.987.

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18

Oh, Byeong-Kweon. "Regular positive ternary quadratic forms." Acta Arithmetica 147, no. 3 (2011): 233–43. http://dx.doi.org/10.4064/aa147-3-3.

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19

Balmer, Paul. "Products of degenerate quadratic forms." Compositio Mathematica 141, no. 06 (2005): 1374–404. http://dx.doi.org/10.1112/s0010437x05001508.

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20

Lewis, D. W. "Hankel matrices and quadratic forms." Linear and Multilinear Algebra 42, no. 4 (1997): 349–63. http://dx.doi.org/10.1080/03081089708818509.

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21

Chapman, Adam, Shira Gilat, and Uzi Vishne. "Linkage of quadratic Pfister forms." Communications in Algebra 45, no. 12 (2017): 5212–26. http://dx.doi.org/10.1080/00927872.2017.1298776.

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22

Marmaridis, N., and J. A. de la Peña. "Quadratic forms and preinjective modules." Journal of Algebra 134, no. 2 (1990): 326–43. http://dx.doi.org/10.1016/0021-8693(90)90056-t.

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23

James, Donald G. "Quadratic forms over polynomial rings." Communications in Algebra 18, no. 1 (1990): 247–51. http://dx.doi.org/10.1080/00927879008823910.

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24

Lewis, D. W., M. G. Mahmoudi, J. P. Tignol, and O. Villa. "Decomposable quadratic forms and involutions." Journal of Algebra 298, no. 2 (2006): 612–29. http://dx.doi.org/10.1016/j.jalgebra.2005.10.030.

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25

Car, M. "Quadratic Forms on F2h[T]." Journal of Number Theory 51, no. 2 (1995): 249–74. http://dx.doi.org/10.1006/jnth.1995.1046.

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26

Simon, Denis. "Solving quadratic equations using reduced unimodular quadratic forms." Mathematics of Computation 74, no. 251 (2005): 1531–44. http://dx.doi.org/10.1090/s0025-5718-05-01729-1.

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27

Shiu, P., and D. A. Buell. "Binary Quadratic Forms, Classical Theory and Modern Computations." Mathematical Gazette 74, no. 469 (1990): 321. http://dx.doi.org/10.2307/3619867.

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28

Reutenauer, Christophe. "On quadratic numbers and forms, and Markoff theory." Journal of Number Theory 227 (October 2021): 265–305. http://dx.doi.org/10.1016/j.jnt.2021.03.005.

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29

Olkin, Ingram, A. M. Mathai, and Serge B. Provost. "Quadratic Forms in Random Variables: Theory and Applications." Journal of the American Statistical Association 87, no. 420 (1992): 1244. http://dx.doi.org/10.2307/2290674.

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30

Harding, E. F., A. M. Matthai, and S. B. Provost. "Quadratic Forms in Random Variables: Theory and Applications." Journal of the Royal Statistical Society. Series A (Statistics in Society) 156, no. 2 (1993): 326. http://dx.doi.org/10.2307/2982749.

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31

Merkur'ev, A. S. "Kaplansky conjecture in the theory of quadratic forms." Journal of Soviet Mathematics 57, no. 6 (1991): 3489–97. http://dx.doi.org/10.1007/bf01100118.

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32

Galkanov, Allaberdi G. "ON QUADRATIC FORMS WITH A STATIONARY HYPERPLANE." RSUH/RGGU Bulletin. Series Information Science. Information Security. Mathematics, no. 3 (2020): 35–46. http://dx.doi.org/10.28995/2686-679x-2020-3-35-46.

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A critical analysis (with specific numerical examples) of the conclusions following from Onsager’s theory in the classical linear thermodynamics of irreversible processes shown the insufficiency of conditions that guarantee the non-negativity and equality to zero of the entropy production. In order to understand the reasons for such a situation, the article introduces the concept of a quadratic form with a stationary hyperplane and compiles a system of nonlinear equations of a special form, in which a Boolean vector is unknown. Their precise definitions are given. The theorem is formulated and

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33

Choie, YoungJu, and Subong Lim. "Construction of Jacobi forms associated to indefinite quadratic forms." Ramanujan Journal 21, no. 1 (2009): 27–39. http://dx.doi.org/10.1007/s11139-008-9153-x.

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34

Schulze-Pillot, Rainer. "Ternary quadratic forms and Brandt matrices." Nagoya Mathematical Journal 102 (June 1986): 117–26. http://dx.doi.org/10.1017/s0027763000000465.

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In a recent paper [9] the author showed (among other results) estimates on the asymptotic behaviour of the representation numbers of positive definite integral ternary quadratic forms, in particular, that for n in a fixed square class tZ2 and lattices L, K in the same spinor genus one has . The main tool utilized for the proof was the theory of modular forms of weight 3/2, especially Shimura’s lifting from the space of cusp forms of weight 3/2 to the space of modular forms of weight 2.

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35

Kim, Mingyu. "Diagonal odd-regular ternary quadratic forms." Journal of Number Theory 224 (July 2021): 67–94. http://dx.doi.org/10.1016/j.jnt.2021.01.014.

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36

Alsina, Montserrat. "Binary quadratic forms and Eichler orders." Journal de Théorie des Nombres de Bordeaux 17, no. 1 (2005): 13–23. http://dx.doi.org/10.5802/jtnb.473.

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37

Friedlander, John, and Henryk Iwaniec. "Ternary quadratic forms with rational zeros." Journal de Théorie des Nombres de Bordeaux 22, no. 1 (2010): 97–113. http://dx.doi.org/10.5802/jtnb.706.

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38

Elsner, Guido. "Values of special indefinite quadratic forms." Acta Arithmetica 138, no. 3 (2009): 201–37. http://dx.doi.org/10.4064/aa138-3-1.

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39

Brent, Barry. "Quadratic minima and modular forms II." Acta Arithmetica 96, no. 4 (2001): 381–87. http://dx.doi.org/10.4064/aa96-4-8.

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40

Zeldich, M. V. "Integral critical and hypercritical quadratic forms." Communications in Algebra 22, no. 9 (1994): 3629–34. http://dx.doi.org/10.1080/00927879408825045.

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41

Arenas, A. "On integral representations by quadratic forms." Linear and Multilinear Algebra 22, no. 2 (1987): 149–60. http://dx.doi.org/10.1080/03081088708817829.

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42

Gerstein, Larry J. "Definite quadratic forms over Fq[x]." Journal of Algebra 268, no. 1 (2003): 252–63. http://dx.doi.org/10.1016/s0021-8693(03)00114-5.

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43

Cha, Byungchul, Emily Nguyen, and Brandon Tauber. "Quadratic forms and their Berggren trees." Journal of Number Theory 185 (April 2018): 218–56. http://dx.doi.org/10.1016/j.jnt.2017.09.003.

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44

Oh, Byeong-Kweon, and Hoseog Yu. "Completely p-primitive binary quadratic forms." Journal of Number Theory 193 (December 2018): 373–85. http://dx.doi.org/10.1016/j.jnt.2018.05.015.

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45

Gerstein, Larry J. "Stretching and welding indecomposable quadratic forms." Journal of Number Theory 37, no. 2 (1991): 146–51. http://dx.doi.org/10.1016/s0022-314x(05)80031-9.

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46

Sun, Zhi-Hong. "Quartic residues and binary quadratic forms." Journal of Number Theory 113, no. 1 (2005): 10–52. http://dx.doi.org/10.1016/j.jnt.2004.11.003.

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47

Sun, Zhi-Hong. "Cubic residues and binary quadratic forms." Journal of Number Theory 124, no. 1 (2007): 62–104. http://dx.doi.org/10.1016/j.jnt.2006.08.001.

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48

Chan, Wai Kiu, and Byeong-Kweon Oh. "Class numbers of ternary quadratic forms." Journal of Number Theory 135 (February 2014): 221–61. http://dx.doi.org/10.1016/j.jnt.2013.08.011.

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49

Shemanske, Thomas R. "Ternary quadratic forms and quaternion algebras." Journal of Number Theory 23, no. 2 (1986): 203–9. http://dx.doi.org/10.1016/0022-314x(86)90090-9.

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50

Hung, D. C. "Theta series of ternary quadratic forms." Journal of Number Theory 26, no. 1 (1987): 1–7. http://dx.doi.org/10.1016/0022-314x(87)90091-6.

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