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Representations by quaternary quadratic forms with coefficients 1, 2, 5 or 10

Ayse Alaca|Mada Altiary
대한수학회 (The Korean Mathematical Society)|2019.01|대한수학회논문집 (Communications of the KMS)|제34권 제1호|pp. 27-41|DOI 10.4134/CKMS.c170468

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참고문헌

키워드

representationstheta functionsmodular formsquaternary quadratic formsDedekind eta functioneta quotientsEisenstein formscusp forms
주제분류수학

초록

We determine explicit formulas for the number of representations of a positive integer $n$ by quaternary quadratic forms with coefficients $1$, $2$, $5$ or $10$. We use a modular forms approach.

Abstract

We determine explicit formulas for the number of representations of a positive integer $n$ by quaternary quadratic forms with coefficients $1$, $2$, $5$ or $10$. We use a modular forms approach.

참고문헌 (21)

  1. A. Alaca, "Nineteen quaternary quadratic forms", Acta Arith, 130(3), pp.277~310 (2007)
  2. A. Alaca, "The number of representations of a positive integer by certain quaternary quadratic forms", Int. J. Number Theory, 5(1), pp.13~40 (2009)
  3. A. Alaca, "On the quaternary forms x2+y2+z2+5t2; x2+y2 +5z2 +5t2 and x2 +5y2 +5z2 +5t2", JP J. Algebra Number Theory Appl, 9(1), pp.37~53 (2007)
  4. A. Alaca, "Representations by quaternary quadratic forms with coecients 1, 2, 7 or 14", Integers, 16(A55), pp.16~ (2016)
  5. B. C. Berndt, "Number Theory in the Spirit of Ramanujan" (2006), American Mathematical Society
  6. B. Gordon, "Multiplicative properties of η-products, in Number theory, Madras 1987, 173-200", Lecture Notes in Math, 1395, pp.173~200 (1987), Springer
  7. C. G. J. Jacobi, "Gesammelte Werke Vol. 1", pp.49~239 (1969), Chelsea
  8. L. J. P. Kilford, "Modular Forms: A Classical and Computational Introduction, second edition" (2015), Imperial College Press
  9. H. D. Kloosterman, "On the representation of numbers in the form ax2+by2+cz2+dt2", Proc. London Math. Soc. (2), 25, pp.143~173 (1926)
  10. G. Köhler, "Eta Products and Theta Series Identities" (2011), Springer
  11. G. Ligozat, "Courbes modulaires de genre 1" (1975), Societe Mathematique de France
  12. J. Liouville, "Sur les deux formes x2 + y2 + 2(z2 + t2)", J. Math. Pures Appl, 5, pp.269~272 (1860)
  13. J. Liouville, "Sur les deux formes x2 +y2 +z2 +2t2 and x2 +2(y2 +z2 +t2)", J. Math. Pures Appl, 6, pp.225~230 (1861)
  14. J. Liouville, "la forme x2 + y2 + z2 + 5t2", J. Math. Pures Appl, 9, pp.1~12 (1864)
  15. J. Liouville, "la forme x2 + 5(y2 + z2 + t2)", J. Math. Pures Appl, 9, pp.17~22 (1864)
  16. J. Liouville, "la forme x2 + y2 + 5z2 + 5t2", J. Math. Pures Appl, 10, pp.1~8 (1865)
  17. G. Lomadse, "Über die Darstellung der Zahlen durch einige quaternare quadratische Formen", Acta Arith, 5, pp.125~170 (1959)
  18. K. Ono, "The web of modularity: arithmetic of the coecients of modular forms and q-series" (2004), Published for the Conference Board of the Mathematical Sciences
  19. W. Stein, "Modular Forms, a Computational Approach" (2007), American Mathematical Society
  20. K. S. Williams, "On the representations of a positive integer by the forms x2+y2+z2+2t2and x2 + 2y2 + 2z2 + 2t2", Int. J. Mod. Math, 3(2), pp.225~230 (2008)
  21. K. S. Williams, "Number Theory in the Spirit of Liouville" (2011), Cambridge University Press

관련 논문AI추천

REPRESENTATIONS BY QUATERNARY QUADRATIC FORMS WITH COEFFICIENTS 1, 2, 11 AND 22Bulent Kokluce대한수학회 · 대한수학회보2023 · 제60권 제1호Representation numbers by quadratic forms of certain levels엄익선대한수학회 · 대한수학회지2024 · 제61권 제6호Fourier coefficients of weight 2 modular forms of prime levelYan-Bin Li대한수학회 · 대한수학회보2021 · 제58권 제3호CUSP FORMS IN S4 (r0 (79)) AND THE NUMBER OF REPRESENTATIONS OF POSITIVE INTEGERS BY SOME DIRECT SUM OF BINARY QUADRATIC FORMS WITH DISCRIMINANT -79Baris Kendirli대한수학회 · 대한수학회보2012 · 제49권 제3호Primitive even 2-regular positive quaternary quadratic forms오병권대한수학회 · 대한수학회지2008 · 제45권 제3호The number of representations of positive integers by positive quadratic formsA. Tekcan, I. Cangül, O. Bizim장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2006 · 제9권 제2호

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