منابع مشابه
Sum-product Estimates in Finite Fields via Kloosterman Sums
We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.
متن کاملSum - Product Estimates
Notes on the sum-product estimates of Bourgain-Katz-Tao and BourgainKonyagin.
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We investigate weighted gcd-sum functions, including the alternating gcd-sum function and those having as weights the binomial coefficients and values of the Gamma function. We also consider the alternating lcm-sum function.
متن کاملThe gcd-sum function
The gcd-sum is an arithmetic function defined as the sum of the gcd’s of the first n integers with n : g(n) = ∑n i=1(i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of par...
متن کاملQuantitative Sum Product Estimates on Different Sets
Let Fp be a finite field of p elements with p prime. In this paper we show that for A,B ⊂ Fp with |B| ≤ |A| < p 1 2 then
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2019
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-019-1932-0