Even equations and Agassiz sums
نویسندگان
چکیده
منابع مشابه
Sums of Even Powers in Archimedean Rings
This note is devoted to the study of totally archimedean rings of regular functions. We easily extend Schm udgen theorem to this class of rings. Moreover, we show that, in such rings, every totally positive element is a sum of even powers of totally positive elements, and hence is a sum of even powers of units.
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Special finite sums of the even powers of the cosecant and of the secant are studied, ∑ k csc (kπ/N) and ∑ k sec (kπ/N), with positive integers N ≥ 3,m and 1 ≤ k < N/2 . The main result of this article is that these power sums are even polynomials in N , of order 2m, whose coefficients are rational. The approach is based on new differential identities for the functions cscz and secz. The Mittag...
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We prove a simple formula for the main value of r-even functions and give applications of it. Considering the generalized Ramanujan sums cA(n, r) involving regular systems A of divisors we show that it is not possible to develop a Fourier theory with respect to cA(n, r), like in the the usual case of classical Ramanujan sums c(n, r).
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P. Wittmann showed that for the irregular coloring number c(G) of a simple 2-regular graph of order n the inequality c(G) 6 √ 2n + O(1) holds. We determine the exact value of this number in the case when the 2-regular graph consists of cycles of even lengths. For this purpose we consider decompositions of several classes of graphs.
متن کاملPrinted Copies: an Even Faster Solver for General Systems of Equations an Even Faster Solver for General Systems of Equations
Electronic copies of technical reports are available: Via FTP: URL ftp://ftp.informatik.uni-trier.de/pub/Users-Root/reports Via WWW: URL http://www.informatik.uni-trier.de/Reports/Current.html Via email: Send a mail to [email protected], subject ’HELP’, for detailed instructions Printed copies: Trierer Forschungsberichte Fachbereich IV Mathematik / Informatik Universitat Trier ..
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1987
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-53-1-9-16