Lower bound for cyclic sums of Diananda type

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A quadratic lower bound for subset sums

Let A be a finite nonempty subset of an additive abelian group G, and let Σ(A) denote the set of all group elements representable as a sum of some subset of A. We prove that |Σ(A)| ≥ |H|+ 1 64 |A \H|2 where H is the stabilizer of Σ(A). Our result implies that Σ(A) = Z/nZ for every set A of units of Z/nZ with |A| ≥ 8√n. This consequence was first proved by Erdős and Heilbronn for n prime, and by...

متن کامل

A Lower Bound for the Optimization of Finite Sums

This paper presents a lower bound for optimizing a finite sum of n functions, where each function is L-smooth and the sum is μ-strongly convex. We show that no algorithm can reach an error ε in minimizing all functions from this class in fewer than Ω(n+ √ n(κ−1) log(1/ε)) iterations, where κ = L/μ is a surrogate condition number. We then compare this lower bound to upper bounds for recently dev...

متن کامل

Tight Lower Bound for the Partial-Sums Problem

This is perhaps one of the most fundamental data structure problems. When the values of A[1, . . . , n] are drawn from a semigroup, its static version (where updates are not allowed) has the famous inverse-Ackermann Θ(α(n)) query bound with linear storage [4]; the dynamic version can be easily solved by a binary tree in O(log n) time per operation, and a corresponding Ω(log n) lower bound was p...

متن کامل

A LeVeque-type Lower Bound for Discrepancy

A sharp lower bound for discrepancy on R/Z is derived that resembles the upper bound due to LeVeque. An analogous bound is proved for discrepancy on R/Z. These are discussed in the more general context of the discrepancy of probablity measures. As applications, the bounds are applied to Kronecker sequences and to a random walk on the torus.

متن کامل

An Improved Mordell Type Bound for Exponential Sums

where ep(·) is the additive character ep(·) = e2πi·/p on the finite field Zp. For χ = χ0, the principal character, the sum is just a pure exponential sum S(χ0, f) = ∑p−1 x=1 ep(f(x)). Of course S(χ, f) = 0 unless χ(p−1)/d = χ0 where d = (k1, ..., kr, p− 1), as is easily seen from the change of variables x → xu if there is a u with u = 1 and χ(u) 6= 1. The classical Weil bound [12] (see [2] or [...

متن کامل

ذخیره 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: Archiv der Mathematik

سال: 2015

ISSN: 0003-889X,1420-8938

DOI: 10.1007/s00013-015-0853-3