Exponential Sum

e Therefore a typical exponential sum may take the form :∑ ''e''(''x''_''n'') summed over a finite sequence of Real Number s ''x''_''n''. If we allow some real coefficients ''a''_''n'', to get the form :∑ ''a''_''n''''e''(''x''_''n''), it is the same as allowing exponents that are Complex Number s. Both forms are certainly useful in applications. A large part of Twentieth Century Analytic Number Theory was devoted to finding good estimates for these sums, a trend started by basic work of Hermann Weyl in Diophantine Approximation . ESTIMATES The main thrust of the subject is that a sum S is ''trivially'' estimated by the number ''N'' of terms. That is, the Absolute Value
	:''S''	O(&radic''N'')
	:''S''	o(''N'')

	CATEGORIES ABOUT EXPONENTIAL SUM

	exponentials

	analytic number theory

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