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Inhomogeneous additive equations.
- Source :
- International Journal of Number Theory; Nov2022, Vol. 18 Issue 10, p2317-2332, 16p
- Publication Year :
- 2022
-
Abstract
- In this paper, we study the function Δ ∗ (k , n) , which we define as the smallest number s of variables needed to guarantee that the equation ∑ i = 1 s a i x i k + ∑ i = 1 s b i y i n = 0 has nontrivial solutions in each of the p -adic fields ℚ p , regardless of the rational integer coefficients. This generalizes the Γ ∗ (k) function of Davenport and Lewis. In this paper, we give a sharp upper bound for Δ ∗ (k , n) and compute its value for various choices of the degrees. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 18
- Issue :
- 10
- Database :
- Complementary Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 158511682
- Full Text :
- https://doi.org/10.1142/S1793042122501184