본문 바로가기
KERD
논문KCI 등재

REPRESENTATIONS BY QUATERNARY QUADRATIC FORMS WITH COEFFICIENTS 1, 2, 11 AND 22

Bulent Kokluce
대한수학회 (The Korean Mathematical Society)|2023.01|대한수학회보 (Bulletin of the KMS)|제60권 제1호|pp. 237-255|DOI 10.4134/BKMS.b220078

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

Eisenstein seriesmodular formsDedekind eta functioncusp formsEta quotientsquadratic formstheta productsrepresentation numbers
주제분류수학

초록

In this article, we find bases for the spaces of modular forms $M_{2}(\Gamma _{0}(88),\big( \frac{d}{\cdot }\big) )$ for $d=1,8,44\text{ and }88$. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients $1,2,11$ and $ 22 $.

Abstract

In this article, we find bases for the spaces of modular forms $M_{2}(\Gamma _{0}(88),\big( \frac{d}{\cdot }\big) )$ for $d=1,8,44\text{ and }88$. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients $1,2,11$ and $ 22 $.

참고문헌 (21)

  1. A. Alaca, "Representations by quaternary quadratic forms with coefficients 1, 3, 5 or 15", Integers, 18(A12), pp.14~ (2018)
  2. Ayşe Alaca, "Theta products and eta quotients of level 24 and weight 2, Funct", Functiones et Approximatio Commentarii Mathematici, 57(2) (2017), Adam Mickiewicz University (Euclid)[DOI]
  3. Ayşe Alaca, "Nineteen quaternary quadratic forms", Acta Arithmetica, 130(3), pp.277~310 (2007), Institute of Mathematics, Polish Academy of Sciences[DOI]
  4. AYŞE ALACA, "THE NUMBER OF REPRESENTATIONS OF A POSITIVE INTEGER BY CERTAIN QUATERNARY QUADRATIC FORMS", International Journal of Number Theory, 05(01), pp.13~40 (2009), World Scientific Pub Co Pte Lt[DOI]
  5. A. Alaca, "Representations by quaternary quadratic forms with coefficients 1, 2, 7 or 14", Integers, 16, pp.16~ (2016)
  6. Ayse Alaca, "Representations by quaternary quadratic forms with coefficients 1, 2, 5 or 10", 대한수학회논문집, 34(1), pp.27~41 (2019), 대한수학회[DOI]
  7. Zafer Selcuk Aygin, "Representations by sextenary quadratic forms with coefficients 1,2,3 and 6 and on newforms in S3(Γ0(24),χ)", Journal of Number Theory, 185, pp.434~448 (2018), Elsevier BV[DOI]
  8. Bruce Berndt, "Student Mathematical Library", pp.34~ (2006), American Mathematical Society
  9. C. G. J. Jacobi, "Gesammelte Werke, Erster Band", pp.49~239 (1969), Chelsea Publishing Co
  10. L. J. P. Kilford, "Modular Forms" (2008), Imperial College Press
  11. G. Kohler, "Springer Monographs in Mathematics" (2011), Springer
  12. Bülent Köklüce, "Representations by certain octonary quadratic forms with coefficients 1, 2, 5 and 10", Proceedings - Mathematical Sciences, 132(2) (2022), Springer Science and Business Media LLC[DOI]
  13. G. Ligozat, "Courbes modulaires de genre 1", Supplement au Bull. Soc. Math. France, 103(3) (1975), Societe Mathematique de France
  14. J. Liouville, "Sur les deux formes x2 + y2 + 2(z2 + t2)", J. Math. Pures Appl, 5, pp.269~272 (1860)
  15. J. Liouville, "Sur les deux formes x2 + y2 + z2 + 2t2, x2 + 2(y2 + z2 + t2)", J. Math. Pures Appl, 6, pp.225~230 (1861)
  16. Morris Newman, "Construction and Application of a Class of Modular Functions†", Proceedings of the London Mathematical Society, s3-7(1), pp.334~350 (1957), Wiley[DOI]
  17. Morris Newman, "Construction and Application of a Class of Modular Functions (II)†", Proceedings of the London Mathematical Society, s3-9(3), pp.373~387 (1959), Wiley[DOI]
  18. W. Stein, "Graduate Studies in Mathematics", pp.79~ (2007), American Mathematical Society
  19. J. Sturm, "On the congruence of modular forms, in Number theory (New York, 1984-1985)", Lecture Notes in Math, 1240, pp.275~280 (1987), Springer
  20. "The L-functions and modular forms database"[URL]
  21. K. S. Williams, "London Mathematical Society Student Texts", pp.76~ (2011), Cambridge University Press

관련 논문AI추천

Representations by quaternary quadratic forms with coefficients 1, 2, 5 or 10Ayse Alaca, Mada Altiary대한수학회 · 대한수학회논문집2019 · 제34권 제1호The 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 제2호CUSP 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 제3호Representation numbers by quadratic forms of certain levels엄익선대한수학회 · 대한수학회지2024 · 제61권 제6호Fourier coefficients of weight 2 modular forms of prime levelYan-Bin Li대한수학회 · 대한수학회보2021 · 제58권 제3호Primitive even 2-regular positive quaternary quadratic forms오병권대한수학회 · 대한수학회지2008 · 제45권 제3호

이 간행물의 다른 논문 (17건)

ON CHOWLA'S HYPOTHESIS IMPLYING THAT L(s, χ) > 0 FOR s > 0 FOR REAL CHARACTERS χStephane R. Louboutinpp. 1-22HOMOLOGY AND SERRE CLASS IN D(R)Zhicheng Wangpp. 23-32S-CURVATURE AND GEODESIC ORBIT PROPERTY OF INVARIANT (α1, α2)-METRICS ON SPHERESShaoxiang Zhang, Zaili Yan, Huihui Anpp. 33-46ON CERTAIN ESTIMATES FOR ROUGH GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALSDaiqing Zhangpp. 47-73MULTIPLICATIVE FUNCTIONS COMMUTABLE WITH BINARY QUADRATIC FORMS x2 ± xy + y2박부성pp. 75-81
원문 보기