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Total: 68 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 ...
2. Graphs with integral spectrum
(Uncategorized/Publication)
It is shown that only a fraction of 2(-Omega(n)) of the graphs on n vertices have an integral spectrum. Although there are several explicit constructions of such graphs, no upper bound for their number ...
Given an elliptic Curve E over Q we estimate the number of primes p  ...
... a more precise form of a result of C. L. Stewart ['On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers', Proc. London Math. Soc. 35(3) (1977), 425-447]. ...
... for a quantum computer-have been demonstrated in several physical architectures. A serious obstacle to a full-scale implementation is the large number of these gates required to build even small quantum ...
6. The entropic boundary law in BF theory
(Uncategorized/Publication)
... bipartite splitting of the graph and show it scales at leading order with the number of vertices on the boundary (or equivalently with the number of loops crossing the boundary). More generally these results ...
7. Arithmetic properties of Apery numbers
(Uncategorized/Publication)
Let (A(n))(n >= 1) be the sequence of Apery numbers with a general term given by http://www.w3.org/. In this paper, we prove that both the inequalities omega(A(n)) > c(0) log log log n and P(A(n)) > c(0) ...
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  ...
We show that for any fixed epsilon > 0, there axe numbers delta > 0 and p(0) >=, 2 with the following property: for every prime p >= p(0) and every integer N such that p(1/(4 root e)+epsilon)  ...
We obtain a new lower bound on the number of prime divisors of integers whose g-ary expansion contains a fixed number of nonzero digits. ...
... of the number of negative eigenvalues of the density matrix. (C) 2007 Elsevier B.V. All rights reserved. ...
... Q(exp(2 pi i/m)) for some P >=(0.3385+o(1)). These results have immediate applications to the divisibility properties of the class number of Q(exp(2 pi i/m)). ...
14. On quadratic fields generated by polynomials
(Uncategorized/Publication)
... formula for the number of distinct fields among Q(root center dot(center dot)) for center dot is an element of\ has recently been given by Cutter, Granville, and Tucker. We use bounds for character sums ...
In this paper we give upper and lower bounds as well as a heuristic estimate on the number of vertices of the convex closure of the set G(n) = f (a, b) : a, b is an element of Z, ab 1 (mod n), 1  ...
For a prime p > 2, an integer a with gcd(a, p) = 1 and 1
We show that, for every x exceeding some explicit bound depending only on k and N, there are at least C(k, N)x/log(17) x positive and negative coefficients a(n) with n = 2 and squarefree level N that is ...
18. 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 ...
... in residue rings. For example, we prove a conjecture of J. Holden and P. Moree on the behavior of the number of solutions to the congruence g(h) = h(mod p), 1  ...
... times resulting from the evolution generated by the strong dipole-dipole interaction. However, for large numbers of atoms in the near-Dicke limit, it is shown that as the number of atoms increases, the ...
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