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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Let Cl denote the cycle of length l. For p > 2 and integer k > 1, we prove that the function
متن کاملDegree powers in graphs with forbidden even cycle
Let Cl denote the cycle of length l: For p 2 and integer k 1; we prove that the function (k; p; n) = max <: X u2V (G) d (u) : G is a graph of order n containing no C2k+2 =; satis es (k; p; n) = knp (1 + o (1)) : This settles a conjecture of Caro and Yuster. Our proof is based on a new su¢ cient condition for long paths, that may be useful in other applications as well.
متن کاملEven Powers of Divisors and Elliptic Zeta Values
We introduce and study elliptic zeta values, a two-parameter deformation of the values of Riemann’s zeta function at positive integers. They are essentially Taylor coefficients of the logarithm of the elliptic gamma function, and share the SL(3,Z) modular properties of this function. Elliptic zeta values at even integers are related to Eisenstein series and thus to sums of odd powers of divisor...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 2019
ISSN: 0137-6934,1730-6299
DOI: 10.4064/bc118-13