Displaying similar documents to “The evaluation of two-dimensional lattice sums via Ramanujan's theta functions”

Diophantine approximation with partial sums of power series

Bruce C. Berndt, Sun Kim, M. Tip Phaovibul, Alexandru Zaharescu (2013)

Acta Arithmetica

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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.

Exponential Sums with Farey Fractions

Igor E. Shparlinski (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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For positive integers m and N, we estimate the rational exponential sums with denominator m over the reductions modulo m of elements of the set ℱ(N) = {s/r : r,s ∈ ℤ, gcd(r,s) = 1, N ≥ r > s ≥ 1} of Farey fractions of order N (only fractions s/r with gcd(r,m) = 1 are considered).