On asymptotic behavior for the Hawkins random sieve
نویسندگان
چکیده
منابع مشابه
On twin primes associated with the Hawkins random sieve
We establish an asymptotic formula for the number of k-difference twin primes associated with the Hawkins random sieve, which is a probabilistic model of the Eratosthenes sieve. The formula for k = 1 was obtained by Wunderlich [Acta Arith. 26 (1974), 59 81]. We here extend this to k ≥ 2 and generalize it to all l-tuples of Hawkins primes.
متن کاملOn Bombieri’s Asymptotic Sieve
If a sequence (an) of non-negative real numbers has “best possible” distribution in arithmetic progressions, Bombieri showed that one can deduce an asymptotic formula for the sum ∑ n≤x anΛk(n) for k ≥ 2. By constructing appropriate sequences, we show that any weakening of the welldistribution property is not sufficient to deduce the same conclusion.
متن کاملAsymptotic sieve for primes
For a long time it was believed that sieve methods might be incapable of achieving the goal for which they had been created, the detection of prime numbers. Indeed, it was shown [S], [B] to be inevitable that, in the sieve’s original framework, no such result was possible although one could come tantalizingly close. This general limitation is recognized as the “parity problem” of sieve theory. ...
متن کاملAsymptotic Behavior of Random Discrete Event Systems
A large class of dynamic systems-such as the material flow in production or assembly lines, the message flow in communication networks, and jobs in computer systems-can be modeled by Discrete Event Dynamic Systems (DEDS). These are systems where the occurrence of events is determined by the system itself and not described by time. Examples of such events are the beginning or completion of a tas...
متن کاملAsymptotic Behavior of Weighted Sums of Weakly Negative Dependent Random Variables
Let be a sequence of weakly negative dependent (denoted by, WND) random variables with common distribution function F and let be other sequence of positive random variables independent of and for some and for all . In this paper, we study the asymptotic behavior of the tail probabilities of the maximum, weighted sums, randomly weighted sums and randomly indexed weighted sums of heavy...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0404177-x