On the number of Abelian groups of a given number.
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G. Kolesnik (1981)
Journal für die reine und angewandte Mathematik
Christopher Hooley (1980)
Journal für die reine und angewandte Mathematik
E. Bombieri, H. Iwaniec (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Steven Sperber, Yasutaka Sibuya (1984/1985)
Groupe de travail d'analyse ultramétrique
Gongrui Chen, Wenxiao Wang (2023)
Czechoslovak Mathematical Journal
Let be a fixed integer. We study the asymptotic formula of , which is the number of positive integer solutions such that the polynomial is -free. We obtained the asymptotic formula of for all . Our result is new even in the case . We proved that , where is a constant depending on . This improves upon the error term obtained by G.-L. Zhou, Y. Ding (2022).
Fernando Chamizo, Henryk Iwaniec (1995)
Revista Matemática Iberoamericana
One of the oldest problems in analytic number theory consists of counting points with integer coordinates in the d-dimensional ball. It is very easy to find a main term for the counting function, but the size of the error term is difficult to estimate (...).
J. C. Peral (1995)
Acta Arithmetica
A. Libgober, S. Sperber (1995)
Compositio Mathematica
H. Iwaniec (1974)
Inventiones mathematicae
Harald Niederreiter, Józef Horbowicz (1988)
Colloquium Mathematicae
Liangyi Zhao (2006)
Revista Matemática Iberoamericana
In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twisted with an exponential sums whose amplitude is √n at prime arguments.
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