A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form

Guodong Hua

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 4, page 1047-1054
  • ISSN: 0011-4642

Abstract

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Let f be a normalized primitive holomorphic cusp form of even integral weight k for the full modular group SL ( 2 , ℤ ) , and denote its n th Fourier coefficient by λ f ( n ) . We consider the hybrid problem of quadratic forms with prime variables and Hecke eigenvalues of normalized primitive holomorphic cusp forms, which generalizes the result of D. Y. Zhang, Y. N. Wang (2017).

How to cite

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Hua, Guodong. "A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form." Czechoslovak Mathematical Journal 72.4 (2022): 1047-1054. <http://eudml.org/doc/298887>.

@article{Hua2022,
abstract = {Let $f$ be a normalized primitive holomorphic cusp form of even integral weight $k$ for the full modular group $\{\rm SL\}(2,\mathbb \{Z\})$, and denote its $n$th Fourier coefficient by $\lambda _\{f\}(n)$. We consider the hybrid problem of quadratic forms with prime variables and Hecke eigenvalues of normalized primitive holomorphic cusp forms, which generalizes the result of D. Y. Zhang, Y. N. Wang (2017).},
author = {Hua, Guodong},
journal = {Czechoslovak Mathematical Journal},
keywords = {circle method; cusp form; Fourier coefficient},
language = {eng},
number = {4},
pages = {1047-1054},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form},
url = {http://eudml.org/doc/298887},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Hua, Guodong
TI - A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 4
SP - 1047
EP - 1054
AB - Let $f$ be a normalized primitive holomorphic cusp form of even integral weight $k$ for the full modular group ${\rm SL}(2,\mathbb {Z})$, and denote its $n$th Fourier coefficient by $\lambda _{f}(n)$. We consider the hybrid problem of quadratic forms with prime variables and Hecke eigenvalues of normalized primitive holomorphic cusp forms, which generalizes the result of D. Y. Zhang, Y. N. Wang (2017).
LA - eng
KW - circle method; cusp form; Fourier coefficient
UR - http://eudml.org/doc/298887
ER -

References

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  1. Calderón, C., Velasco, M. J. de, 10.1007/BF01377596, Bol. Soc. Bras. Mat., Nova Sér. 31 (2000), 81-91. (2000) Zbl1031.11057MR1754956DOI10.1007/BF01377596
  2. Chamizo, F., Iwaniec, H., 10.4171/RMI/178, Rev. Mat. Iberoam. 11 (1995), 417-429. (1995) Zbl0837.11054MR1344899DOI10.4171/RMI/178
  3. Chen, J., Improvement of asymptotic formulas for the number of lattice points in a region of three dimensions. II, Sci. Sin. 12 (1963), 751-764. (1963) Zbl0127.27503MR0186632
  4. Deligne, P., 10.1007/BF02684373, Publ. Math., Inst. Hautes Étud. Sci. 43 (1974), 273-307 French. (1974) Zbl0287.14001MR0340258DOI10.1007/BF02684373
  5. Friedlander, J. B., Iwaniec, H., 10.1007/s11511-009-0033-z, Acta Math. 202 (2009), 1-19. (2009) Zbl1278.11089MR2486486DOI10.1007/s11511-009-0033-z
  6. Guo, R., Zhai, W., 10.4064/aa156-2-1, Acta Arith. 156 (2012), 101-121. (2012) Zbl1270.11099MR2997561DOI10.4064/aa156-2-1
  7. Heath-Brown, D. R., Lattice points in the sphere, Number Theory in Progress. Vol. 2 de Gruyter, Berlin (1999), 883-892. (1999) Zbl0929.11040MR1689550
  8. Hu, G., Jiang, Y., Lü, G., 10.1112/mtk.12006, Mathematika 66 (2020), 39-55. (2020) Zbl1470.11082MR4130311DOI10.1112/mtk.12006
  9. Hu, G., Lü, G., 10.1016/j.jnt.2020.08.009, J. Number Theory 220 (2021), 61-74. (2021) Zbl1466.11065MR4177535DOI10.1016/j.jnt.2020.08.009
  10. Hu, L., Yang, L., 10.4064/aa170120-20-10, Acta Arith. 183 (2018), 63-85. (2018) Zbl1428.11170MR3774393DOI10.4064/aa170120-20-10
  11. Hua, L.-K., 10.1093/qmath/os-9.1.199, Q. J. Math., Oxf. Ser. 9 (1938), 199-202. (1938) Zbl0020.10504DOI10.1093/qmath/os-9.1.199
  12. Ren, X., 10.1360/03ys0341, Sci. China, Ser. A 48 (2005), 785-797. (2005) Zbl1100.11025MR2158973DOI10.1360/03ys0341
  13. Sun, Q., Zhang, D., 10.1016/j.jnt.2016.04.010, J. Number Theory 168 (2016), 215-246. (2016) Zbl1396.11117MR3515816DOI10.1016/j.jnt.2016.04.010
  14. Vaughan, R. C., 10.1017/CBO9780511470929, Cambridge Tracts in Mathematics 125. Cambridge University Press, Cambridge (1997). (1997) Zbl0868.11046MR1435742DOI10.1017/CBO9780511470929
  15. Vinogradov, I. M., On the number of integer points in a sphere, Izv. Akad. Nauk SSSR, Ser. Mat. 27 (1963), 957-968 Russian. (1963) Zbl0116.03901MR0156821
  16. Zhang, D., Wang, Y., 10.1016/j.jnt.2016.12.018, J. Number Theory 176 (2017), 211-225. (2017) Zbl1422.11100MR3622128DOI10.1016/j.jnt.2016.12.018
  17. Zhao, L., 10.4064/aa163-2-6, Acta Arith. 163 (2014), 161-177. (2014) Zbl1346.11056MR3200169DOI10.4064/aa163-2-6

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