A Paucity Estimate Related to Newton Sums of Odd Degree
نویسنده
چکیده
Paucity is established for a system of diagonal diophantine equations, in which the degrees are the odd numbers in ascending order. §
منابع مشابه
m at h . N T ] 1 8 Ju n 20 07 NEWTON POLYGONS FOR TWISTED EXPONENTIAL SUMS AND POLYNOMIALS
We study the p-adic absolute value of the roots of the L-functions associated to certain twisted character sums, and additive character sums associated to polynomials P (x d), when P varies among the space of polynomial of fixed degree e over a finite field of characteristic p. For sufficiently large p, we determine in both cases generic Newton polygons for these L-functions, which is a lower b...
متن کاملNewton Polygons for Twisted Exponential Sums
We study the p-adic absolute value of the roots of the L-functions associated to certain twisted character sums, and additive character sums associated to polynomials P (x d), when P varies among the space of polynomial of fixed degree e over a finite field of characteristic p. For sufficiently large p, we determine in both cases generic Newton polygons for these L-functions, which is a lower b...
متن کاملError estimation of fuzzy Newton-Cotes method for Integration of fuzzy functions
Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...
متن کاملFactors of binomial sums from the Catalan triangle
By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial coefficients and an odd power of a natural number. For example, we prove that for all positive integers n1, . . . , nm, nm+1 = n1, and any nonnegative integer...
متن کاملEqual sums of like polynomials
Let f ∈ Z[x] be a polynomial of degree d. We establish the paucity of non-trivial positive integer solutions to the equation f(x1) + f(x2) = f(x3) + f(x4), provided that d ≥ 7. We also investigate the corresponding situation for equal sums of three like polynomials. Mathematics Subject Classification (2000): 11D45 (11P05)
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012