|
In mathematics, Turán's method provides lower bounds for exponential sums and complex power sums. The method has been applied to problems in equidistribution. The method applies to sums of the form : where the ''b'' and ''z'' are complex numbers and ''ν'' runs over a range of integers. There are two main results, depending on the size of the complex numbers ''z''. ==Turán's first theorem== The first result applies to sums ''s''ν where for all ''n''. For any range of ''ν'' of length ''N'', say ''ν'' = ''M'' + 1, ..., ''M'' + ''N'', there is some ''ν'' with |''s''''ν''| at least ''c''(''M'', ''N'')|''s''0| where : The sum here may be replaced by the weaker but simpler . We may deduce the Fabry gap theorem from this result. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Turán's method」の詳細全文を読む スポンサード リンク
|