Signed sums of polynomial values
نویسندگان
چکیده
منابع مشابه
Reducibility of Signed Cyclic Sums of Mordell-tornheim Zeta and L-values
Matsumoto et al. define the Mordell-Tornheim L-functions of depth k by LMT(s1, . . . , sk+1;χ1, . . . , χk+1) := ∞ ∑
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(1.2) f(x) = a1x k1 + · · ·+ arx with 0 < k1 < k2 < · · · < kr. We assume always that the content of f , (a1, a2, . . . , ar), is relatively prime to the modulus q. Let d = d(f) = kr denote the degree of f and for any prime p let dp(f) denote the degree of f read modulo p. A fundamental problem is to determine whether there exists an absolute constant C such that for an arbitrary positive integ...
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where A(α, k) is the number of permutations of the numbers 1 to α in which exactly k elements are greater than the previous element (the so-called Eulerian numbers), provided we define A(α,−1) to be equal to zero if α > 0 and equal to one if α = 0. Proof. We achieve immediate simplification by linearity, so we only have to deal with one monomial at a time, and in the case of a monomial the mult...
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with unknown xi. In 1769 Euler conjectured that (1.1) has no positive integral solutions when m < n. This generalizes both his result for n1⁄4 3 and Fermat’s Last Theorem. However his conjecture was refuted for mþ 11⁄4 n1⁄4 5 (Lander and Parkin, 1966) and then for mþ 11⁄4 n1⁄4 4 (Elkies, 1988). It is still unknown whether (1.1) has solutions with mþ 11⁄4 n 6 or with m1⁄4 31⁄4 n 2. On the other ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2001
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-01-06461-9