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FOURIER COEFFICIENTS OF WEIGHT 2 MODULAR FORMS OF PRIME LEVEL

  • Li, Yan-Bin (School of Mathematical Sciences Tongji University)
  • Received : 2020.04.24
  • Accepted : 2021.02.09
  • Published : 2021.05.31

Abstract

We use a kind of modified Hurwitz class numbers to express the number of representing a positive integer by some ternary quadratic forms such as the sum of three squares, and the Fourier coefficients of weight 2 modular forms of prime level with trivial character.

Keywords

References

  1. A. O. L. Atkin and J. Lehner, Hecke operators on Γ0(m), Math. Ann. 185 (1970), 134-160. https://doi.org/10.1007/BF01359701
  2. H. Boylan, N.-P. Skoruppa, and H. Zhou, Counting zeros in quaternion algebras using Jacobi forms, Trans. Amer. Math. Soc. 371 (2019), no. 9, 6487-6509. https://doi.org/10.1090/tran/7575
  3. H. Cohen and F. Stromberg, Modular forms, Graduate Studies in Mathematics, 179, American Mathematical Society, Providence, RI, 2017. https://doi.org/10.1090/gsm/179
  4. B. H. Gross, Heights and the special values of L-series, in Number theory (Montreal, Que., 1985), 115-187, CMS Conf. Proc., 7, Amer. Math. Soc., Providence, RI, 1987.
  5. A. Pizer, An algorithm for computing modular forms on Γ0(N), J. Algebra 64 (1980), no. 2, 340-390. https://doi.org/10.1016/0021-8693(80)90151-9