Sums of arithmetic functions over values of binary forms
نویسندگان
چکیده
منابع مشابه
Sums of Arithmetic Functions over Values of Binary Forms
Given a suitable arithmetic function h : N → R>0, and a binary form F ∈ Z[x1, x2], we investigate the average order of h as it ranges over the values taken by F . A general upper bound is obtained for this quantity, in which the dependence upon the coefficients of F is made completely explicit.
متن کاملPowerfree Values of Binary Forms
Given a binary form f(x; y) 2 Z[x; y], we will be interested in nding the smallest k for which we can establish that there are in nitely many integers a and b such that f(a; b) is k free. Necessarily, we require the f has no xed kth prime power divisor. Until the nal section of this paper, we will also consider f to be irreducible. We set n = deg f . For k = 2, this problem has recently become ...
متن کاملOn Character Sums of Binary Quadratic Forms
We establish character sum bounds of the form ∣∣∣∣ ∑ a≤x≤a+H b≤y≤b+H χ(x + ky) ∣∣∣∣ < p−τH2, where χ is a nontrivial character (mod p), p 1 4 +ε < H < p, and |a|, |b| < p H. As an application, we obtain that given k ∈ Z\{0}, x + k is a quadratic non-residue (mod p) for some 1 ≤ x < p 1 2e. Introduction. Let k be a nonzero integer. Let p be a large prime and let H ≤ p. We are interested in the c...
متن کاملOn Equal Values of Power Sums of Arithmetic Progressions
In this paper, we consider the Diophantine equation b + (a+ b) + · · ·+ (a (x− 1) + b) = = d + (c+ d) + · · ·+ (c (y − 1) + d) , where a, b, c, d, k, l are given integers with gcd(a, b) = gcd(c, d) = 1, k 6= l. We prove that, under some reasonable assumptions, the above equation has only finitely many solutions.
متن کاملMoment Sums Associated with Binary Linear Forms
A transparent argument is used to study the structure of the set of numbers representable as ax + by, with x, y ≥ 0. Moment sums of representable numbers are evaluated in terms of Bernoulli numbers.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2006
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa125-3-6