Article
| Title: | A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form (English) |
| Author: | Hua, Guodong |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 1047-1054 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | 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). (English) |
| Keyword: | circle method |
| Keyword: | cusp form |
| Keyword: | Fourier coefficient |
| MSC: | 11F30 |
| MSC: | 11F41 |
| MSC: | 11N37 |
| idZBL: | Zbl 07655781 |
| idMR: | MR4517594 |
| DOI: | 10.21136/CMJ.2022.0329-21 |
| . | |
| Date available: | 2022-11-28T11:36:22Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151128 |
| . | |
| Reference: | [1] Calderón, C., Velasco, M. J. de: On divisors of a quadratic form.Bol. Soc. Bras. Mat., Nova Sér. 31 (2000), 81-91. Zbl 1031.11057, MR 1754956, 10.1007/BF01377596 |
| Reference: | [2] Chamizo, F., Iwaniec, H.: On the sphere problem.Rev. Mat. Iberoam. 11 (1995), 417-429. Zbl 0837.11054, MR 1344899, 10.4171/RMI/178 |
| Reference: | [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. Zbl 0127.27503, MR 0186632 |
| Reference: | [4] Deligne, P.: La conjecture de Weil. I.Publ. Math., Inst. Hautes Étud. Sci. 43 (1974), 273-307 French. Zbl 0287.14001, MR 0340258, 10.1007/BF02684373 |
| Reference: | [5] Friedlander, J. B., Iwaniec, H.: Hyperbolic prime number theorem.Acta Math. 202 (2009), 1-19. Zbl 1278.11089, MR 2486486, 10.1007/s11511-009-0033-z |
| Reference: | [6] Guo, R., Zhai, W.: Some problems about the ternary quadratic form $m_{1}^{2}+m_{2}^{2}+m_{3}^{2}$.Acta Arith. 156 (2012), 101-121. Zbl 1270.11099, MR 2997561, 10.4064/aa156-2-1 |
| Reference: | [7] Heath-Brown, D. R.: Lattice points in the sphere.Number Theory in Progress. Vol. 2 de Gruyter, Berlin (1999), 883-892. Zbl 0929.11040, MR 1689550 |
| Reference: | [8] Hu, G., Jiang, Y., Lü, G.: The Fourier coefficients of $\Theta$-series in arithmetic progressions.Mathematika 66 (2020), 39-55. Zbl 1470.11082, MR 4130311, 10.1112/mtk.12006 |
| Reference: | [9] Hu, G., Lü, G.: Sums of higher divisor functions.J. Number Theory 220 (2021), 61-74. Zbl 1466.11065, MR 4177535, 10.1016/j.jnt.2020.08.009 |
| Reference: | [10] Hu, L., Yang, L.: Sums of the triple divisor function over values of a quaternary quadratic form.Acta Arith. 183 (2018), 63-85. Zbl 1428.11170, MR 3774393, 10.4064/aa170120-20-10 |
| Reference: | [11] Hua, L.-K.: On Waring's problem.Q. J. Math., Oxf. Ser. 9 (1938), 199-202. Zbl 0020.10504, 10.1093/qmath/os-9.1.199 |
| Reference: | [12] Ren, X.: On exponential sums over primes and application in Waring-Goldbach problem.Sci. China, Ser. A 48 (2005), 785-797. Zbl 1100.11025, MR 2158973, 10.1360/03ys0341 |
| Reference: | [13] Sun, Q., Zhang, D.: Sums of the triple divisor function over values of a ternary quadratic form.J. Number Theory 168 (2016), 215-246. Zbl 1396.11117, MR 3515816, 10.1016/j.jnt.2016.04.010 |
| Reference: | [14] Vaughan, R. C.: The Hardy-Littlewood Method.Cambridge Tracts in Mathematics 125. Cambridge University Press, Cambridge (1997). Zbl 0868.11046, MR 1435742, 10.1017/CBO9780511470929 |
| Reference: | [15] Vinogradov, I. M.: On the number of integer points in a sphere.Izv. Akad. Nauk SSSR, Ser. Mat. 27 (1963), 957-968 Russian. Zbl 0116.03901, MR 0156821 |
| Reference: | [16] Zhang, D., Wang, Y.: Ternary quadratic form with prime variables attached to Fourier coefficients of primitive holomorphic cusp form.J. Number Theory 176 (2017), 211-225. Zbl 1422.11100, MR 3622128, 10.1016/j.jnt.2016.12.018 |
| Reference: | [17] Zhao, L.: The sum of divisors of a quadratic form.Acta Arith. 163 (2014), 161-177. Zbl 1346.11056, MR 3200169, 10.4064/aa163-2-6 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
