HUA’S THEOREM WITH FIVE ALMOST EQUAL PRIME VARIABLES

It is proved that each sufficiently large integer N ≡ 5 (mod24) can be written as N=p12+p22+p23+p24+p25 with|pj-√N/5| ≤ U = N1/2- 1/35+ε, where pj are primes. This result, which is obtained by an iterative method and a hybrid estimate for Dirichlet polynomial, improves the previous results in this direction.     

HUA’S THEOREM WITH FIVE ALMOSTE QUAL PRIME VARIABLES

§1. IntroductionIn the additive theory of prime numbers, one studies the representation of positive in-tegers by powers of primes. For the quadratic case, Hua [1] proved that each large integercongruent to 5 modulo 24 can be written as the sum of ?ve squ…     

AMBARZUMYAN’S THEOREM WITH EIGENPARAMETER IN THE BOUNDARY CONDITIONS

In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spectrum of the operator D 2 +q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.