|
Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 116, Pages 86–95
(Mi znsl1754)
|
|
|
|
This article is cited in 1 scientific paper (total in 1 paper)
Some analogies of the Hardy–Littlewood equation
F. B. Koval'chik
Abstract:
We derive an asymptotic expansion for the number of representations of an integer $\mathscr N$ in the form
$$
\mathscr N=\ell_1(p,q)+\ell_2(x,y),
$$
where $p,q$ are odd primes, $x,y$ are integers, $\ell _1$ and $\ell_2$ are arbitrary primitive quadratic forms with negative discriminant. The equation $\mathscr N=p^2+q^2+x^2+y^2$ was studied earlier by V. A. Plaksin (RZhMat, 1981, 8A135) who used the methods of C. Hooley (RZhMat, 1958, 5451) and Linnik's dispersion method. The author follows Hooley without the use of the dispersion method. The proof is relatively simple.
Citation:
F. B. Koval'chik, “Some analogies of the Hardy–Littlewood equation”, Integral lattices and finite linear groups, Zap. Nauchn. Sem. LOMI, 116, "Nauka", Leningrad. Otdel., Leningrad, 1982, 86–95; J. Soviet Math., 26:3 (1984), 1887–1894
Linking options:
https://www.mathnet.ru/eng/znsl1754 https://www.mathnet.ru/eng/znsl/v116/p86
|
Statistics & downloads: |
Abstract page: | 183 | Full-text PDF : | 41 |
|