Partial sums of  modulo 1.

Vinson, Jade

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We study the question: How often do partial sums of power series of functions coalesce with convergents of the (simple) continued fractions of the functions? Our theorems quantitatively demonstrate that the answer is: not very often. We conjecture that in most cases there are only a finite number of partial sums coinciding with convergents. In many of these cases, we offer exact numbers in our conjectures.

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We analyze various generalized two-dimensional lattice sums, one of which arose from the solution to a certain Poisson equation. We evaluate certain lattice sums in closed form using results from Ramanujan's theory of theta functions, continued fractions and class invariants. Many explicit examples are given.

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Displaying similar documents to “Partial sums of ζ ( 1 2 ) modulo 1.”

Displaying similar documents to “Partial sums of $ζ (\frac{1}{2})$ modulo 1.”