منابع مشابه
Mean Value of Hardy Sums over Short Intervals
The main purpose of this paper is to study the mean value properties of certain Hardy sums over short intervals by using the mean value theorems of the Dirichlet L-functions, and to give two interesting asymptotic formulae.
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The purpose of this paper is to obtain a bound for sums of Hecke series in short intervals which, as a by-product, gives a new bound for Hj( 1 2 ). We begin by stating briefly the necessary notation and some results involving the spectral theory of the non-Euclidean Laplacian. For a competent and extensive account of spectral theory the reader is referred to Y. Motohashi’s monograph [13]. Let {...
متن کاملSums of Two Squares in Short Intervals in Polynomial Rings over Finite Fields
Landau’s theorem asserts that the asymptotic density of sums of two squares in the interval 1 ≤ n ≤ x is K/ √ log x, where K is the Landau-Ramanujan constant. It is an old problem in number theory whether the asymptotic density remains the same in intervals |n− x| ≤ x for a fixed and x→∞. This work resolves a function field analogue of this problem, in the limit of a large finite field. More pr...
متن کاملIncomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals
We investigate the solubility of the congruence xy ≡ 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2009.03.031