On the Hooley’s problem on the representation of a number as the sum of a square and a product
- Authors: Bykovskii V.A.1, Ustinov A.V.1
-
Affiliations:
- Pacific National University
- Issue: Vol 485, No 5 (2019)
- Pages: 539-544
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/14282
- DOI: https://doi.org/10.31857/S0869-56524855539-544
- ID: 14282
Cite item
Full Text
Abstract
The article is devoted to the Hooley’s problem on the representation of a number as the sum of a square and a product. For the first time we show that number of solutions satisfy an asymptotic formula with power saving in error term.
About the authors
V. A. Bykovskii
Pacific National University
Author for correspondence.
Email: vab@iam.khv.ru
Corresponding Member of the Russian Academy of Sciences
Russian Federation, 136, Tikhookeanskaya street, Khabarovsk, 680035A. V. Ustinov
Pacific National University
Email: ustinov@iam.khv.ru
Russian Federation, 136, Tikhookeanskaya street, Khabarovsk, 680035
References
- Hooley C. On the Representation of a Number as the Sum of a Square and a Product // Math. Zeitschr. 1958. Bd. 69. P. 211-217. 2. Иванец Х., Ковальский Э. Аналитическая теория чисел. М.: МЦНМО, 2014. 712 с.
- Motohashi Y. Spectral Theory of the Riemann Zeta-Function. Cambridge: Cambridge Univ. Press, 1997. 240 p.
- Zagier D. Eisenstein Series and the Riemann Zeta-Function. In: Automorphic Forms, Representation Theory and Arithmetic. Bombay: Tata Inst., 1979. P. 275-901.
- Shintani T. On Construction of Holomorphic Cups Forms of Half-Integral Weight // Nagoya Math. J. 1975. V. 58. P. 83-126.
- Kohnen W. Fourier Coefficients of Modular Forms of Half-Integral Weight // Math. Ann. 1985. V. 271. № 2. P. 237-268.
- Быковский В. А. Некоторые формулы суммирования арифметического типа и их приложения. Владивосток: Вычисл. центр ДВНЦ АН СССР, 1986. 40 с.
- Быковский В. А. Арифметические средние и L-ряды автоморфных форм. Хабаровск: Изд-во Тихоокеан. гос. ун-та, 2017. 68 с.
- Градштейн И. С., Рыжик И. М. Таблицы интегралов, сумм, рядов и произведений. М.: Наука, 1971. 1108 с.
- Duke W. Hyperbolic Distribution Problems and Half-Integral Weight // Invent. Math. 1988. V. 92. P. 73-90.
- Blomer V., Harcos G. Hybrid Bounds for Twisted L Finctions // J. Reine Angew. Math. 2008. V. 621. P. 53-79.