Diophantine approximation with partial sums of power series

• Autorzy: Bruce C. Berndt , Sun Kim , M. Tip Phaovibul , Alexandru Zaharescu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11J68: Approximation to algebraic numbers
• 11J70: Continued fractions and generalizations
• 11J17: Approximation by numbers from a fixed field

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 3
• Strony: 249-266

Daty

wydano

2013

Twórcy

autor

Bruce C. Berndt

• Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, IL 61801, U.S.A.

autor

Sun Kim

• Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, U.S.A.

autor

M. Tip Phaovibul

• Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, IL 61801, U.S.A.

autor

Alexandru Zaharescu

• Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, IL 61801, U.S.A.
• Institute of Mathematics of the, Romanian Academy, P.O. Box 1-764, Bucureşti RO-70700, Romania

Identyfikatory

DOI

10.4064/aa161-3-4