It has been shown recently that the amplitude of the creation of n real scalar particles by one virtual boson near n–particle threshold exhibits exponential behavior at n ∼ 1/λ. We extend this result to the processes of multiparticle production at threshold by two virtual bosons. We find that both the tree–level amplitude and leading–n loop corrections have the same exponential behavior, with t...

It is well-known that there is an efficient method for decrypting/signing with RSA when the secret exponent d is small modulo p− 1 and q − 1. We call such an exponent d a small CRT-exponent. It is one of the major open problems in attacking RSA whether there exists a polynomial time attack for small CRT-exponents, i.e. a result that can be considered as an equivalent to the Wiener and Boneh-Dur...

We discuss the shape dependence of the finite-size scaling limit in a strongly anisotropic O(N) model in the large-N limit. We show that scaling is observed even if an incorrect value for the anisotropy exponent is considered. However, the related exponents may only be effective ones, differing from the correct critical exponents of the model. We discuss the implications of our results for nume...

We conjecture the exact scaling theory for the adsorption of two-dimensional polymers by using boundary S matrices. We compute the boundary free energy (the “g-function”), study the flow from adsorbed to desorbed phase, and derive the crossover exponent and all the geometrical exponents at the transition. More generally, we solve the special transition in the O(n) model, the polymer case corres...

Abstract. We are studying the Diophantine exponent μn,l defined for integers 1 ≤ l < n and a vector α ∈ R by letting μn,l = sup{μ ≥ 0 : 0 < ‖x · α‖ < H(x) for infinitely many x ∈ Cn,l ∩ Zn}, where · is the scalar product and ‖ · ‖ denotes the distance to the nearest integer and Cn,l is the generalised cone consisting of all vectors with the height attained among the first l coordinates. We show...

It is well-known that there is an efficient method for decrypt-ing/signing with RSA when the secret exponent d is small modulo p− 1and q − 1. We call such an exponent d a small CRT-exponent. It is one of the major open problems in attacking RSA whether there exists a polynomial time attack for small CRT-exponents, i.e. a result that can be considered as an equivalent to the Wiener and B...

We show a Θ(n log n) bound on the maximal number of occurrences of primitively-rooted k-th powers occurring in a string of length n for any integer k, k ≥ 2. We also show a Θ(n) bound on the maximal number of primitively-rooted powers with fractional exponent e, 1 < e < 2, occurring in a string of length n. This result holds obviously for their maximal number of occurrences. The first result co...

The relation between the household electrical consumption Y and population N for Chinese cities in 2006 has been investigated with the power law scaling form Y = A0N β . It is found that the Chinese cities should be divided into three categories characterized by different scaling exponent β. The first category, which includes the biggest and coastal cities of China, has the scaling exponent β >...