A paucity problem for certain triples of diagonal equations
نویسندگان
چکیده
We consider certain systems of three linked simultaneous diagonal equations in ten variables with total degree exceeding five. By means a complification argument, we obtain an asymptotic formula for the number integral solutions this system bounded height that resolves associated paucity problem.
منابع مشابه
Certain diagonal equations over finite fields
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
متن کاملExistence and Uniqueness of Solutions of Certain Systems of Algebraic Equations with off Diagonal Nonlinearity
Using inverse positivity properties and Brouwer’s fixed point theorem, we derive existence and uniqueness results for certain nonlinear systems of equations with off diagonal nonlinearity. The type of systems considered arises from stable finite volume discretizations of viscous nonlinear conservation laws and has a wide range of applications.
متن کاملInvariant Subspaces for Certain Finite-rank Perturbations of Diagonal Operators
Suppose that {ek} is an orthonormal basis for a separable, infinite-dimensional Hilbert space H. Let D be a diagonal operator with respect to the orthonormal basis {ek}. That is, D = ∑∞ k=1 λkek⊗ek, where {λk} is a bounded sequence of complex numbers. Let T = D + u1 ⊗ v1 + · · ·+ un ⊗ vn. Improving a result [2] of Foias et al., we show that if the vectors u1, . . . , un and v1, . . . , vn satis...
متن کاملGreen function diagonal for a class of heat equations
A construction of the heat kernel diagonal is considered as element of generalized Zeta function, that, being meromorfic function, its gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expression in the case of finite-gap potential coefficient of the heat equation are constructed.
متن کاملA New Method for Certain Diophantine Equations
1. Introduction. The original purpose of the research described in this article was to obtain results about Diophantine problems on rational surfaces — that is, surfaces defined over a field k which are birationally equivalent to P 2 over the algebraic closure ¯ k. (Throughout this article, K and k will always denote algebraic number fields, with respective rings of integers O and o. Except in ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of The London Mathematical Society
سال: 2022
ISSN: ['1469-2120', '0024-6093']
DOI: https://doi.org/10.1112/blms.12636