Mean Value Theorems

Wang Yuan
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Wang Yuan: Academia Sinica, Institute of Mathematics

Chapter Chapter 4 in Diophantine Equations and Inequalities in Algebraic Number Fields, 1991, pp 44-57 from Springer

Abstract: Abstract Let $$ f\left( \lambda \right) = {{\alpha }_{k}}{{\lambda }^{k}} + \cdots + {{\alpha }_{1}}\lambda $$ be a polynomial of k-th degree with coefficients in J, where $${{\alpha }_{i}} \in M\left( {O({{T}^{{k - i}}})} \right), 1 \leqslant i \leqslant k$$ Let $$ s\left( {f\left( \lambda \right)} \right),\xi ,{\text{T}} = s\left( {f,{\text{T}}} \right) = \sum\limits_{\lambda \in M'\left( T \right)} {E\left( {f\left( \lambda \right)\xi } \right),} $$ where we use M’(T) to denote subset of M(T) which may be distinct in different occurances.

Date: 1991
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DOI: 10.1007/978-3-642-58171-7_4

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