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Total: 60 results found.

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1. BILINEAR SUMS WITH EXPONENTIAL FUNCTIONS
(Uncategorized/Publication)
Let g not equal 0, +/- 1 be a fixed integer. Given two sequences of complex numbers (phi(m))(m=1)(infinity) and (psi(n))(n=1)(infinity) and two sufficiently large integers M and N, we estimate the exponential ...
We give upper bounds for sums of multiplicative characters modulo an integer q >= 2 with the Euler function phi (n) and with the shifted largest prime divisor P(n) + a of integers n  ...
Let q >= 2 and N >= 1 be integers. W. Zhang recently proved that for any fixed epsilon > 0 and q(epsilon)
4. On the Values of Kloosterman Sums
(Uncategorized/Publication)
... Charpin and G. Gong which in turn were motivated by some applications to bent functions. ...
... coiling, to realize a linearly-polarized fiber laser with a low birefringence fiber cavity. We show that the polarization-dependent grating strength is a function of the writing pulse energy and that only ...
... for monotonicity, in particular that a function must be non-increasing under local operations and classical communications. ...
We view an algebraic curve over Q as providing a one-parameter family of number fields and obtain bounds for the average value of some standard prime ideal counting functions over these families which ...
We give bounds on the number of integers 1
Anyons are particlelike excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wave function, generalizing Bose and Fermi statistics, ...
10. On the distribution of Kloosterman sums
(Uncategorized/Publication)
... v for u epsilon U, v epsilon V for any two sufficiently large sets U, V subset of F-p(*). We also improve a recent bound on the nonlinearity of a Boolean function associated with the sequence of signs ...
11. On the values of the divisor function
(Uncategorized/Publication)
For a positive integer n we let tau(n) denote the number of its positive divisors. In this paper, we obtain lower and upper bounds for the average value of the ratio tau(n + 1)/tau(n) as n ranges through ...
We obtain asymptotic formulas for all the moments of certain arithmetic functions with linear recurrence sequences. We also apply our results to obtain asymptotic formulas for some mean values related ...
We estimate Fourier coefficients of a Boolean function which has recently been introduced in the study of read-once branching programs. Our bound implies that this function has rather ``flat'' Fourier ...
We show that the communication complexity of the parity of the sum of binary digits of x + y is at least 0.085667...n + O(1) where x and y are n-bit integers. We also obtain a nontrivial (but weaker) lower ...
15. Fluidic fibre dye lasers
(Uncategorized/Publication)
... the chromophore density in the liquid core and a functional wavelength selectivity mechanism inherent in both types of lasers provided a long free spectral range that does not correspond to the length ...
16. Least totient in a residue class
(Uncategorized/Publication)
For a given residue class a (mod m) with gcd(a, m) = 1, upper bounds are obtained on the smallest value of n with phi(n) equivalent to a (mod m). Here, as usual phi(n) denotes the Euler function. These ...
17. On rough and smooth neighbors
(Uncategorized/Publication)
We study the behavior of the arithmetic functions defined by F(n) = P+(n)/P-(n+1) and G(n) = P+(n + 1)/P-(n) (n >= 1), where P+(k) and P-(k) denote the largest and the smallest prime factors, respectively, ...
Let P denote the set of prime numbers, and let P (n) denote the largest prime factor of an integer n > 1. We show that, for every real number 32/17 < eta < (4 + 3 root 2)/4, there exists a constant c(eta) ...
19. Prime divisors in Beatty sequences
(Uncategorized/Publication)
We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence [alpha n + beta], n = 1, 2,..., where alpha, beta is an element of R, and alpha > 0 is irrational. ...
... except in certain trivial cases, unambiguous discrimination among all standard oracle operators corresponding to integer functions with fixed domain and range is impossible. However, we find that it is ...
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