There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinatorial number theory, exact formulas for number-theoretic quantities are derived from relations between analytic functions. Elliptic functions, especially theta functions, are an important class of such functions in this context, which had been made clear already in Jacobi's Fundamenta nova.
Wordweb Threasures & Dictionary for iphone & ipod touch
Added by: secretprince | Karma: 9.08 | Black Hole | 17 December 2009
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Wordweb Threasures & Dictionary for iphone & ipod touch
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One focus of study in generative syntactic theory concerns the constraints on the distribution of 'empty categories,' syntactically empty positions, which are either derived through movement.