On regularity of small primes in function fields
نویسندگان
چکیده
منابع مشابه
Strings of Consecutive Primes in Function Fields
In a recent paper, Thorne [5] proved the existence of arbitrarily long strings of consecutive primes in arithmetic progressions in the polynomial ring Fq[t]. Here we extend this result to show that given any k there exists a string of k consecutive primes of degree D in arithmetic progression for all sufficiently large D.
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We adapt the Maier matrix method to the polynomial ring Fq[t], and prove analogues of results of Maier [4] and Shiu [10] concerning the distribution of primes in short intervals.
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Let p be an odd prime, such that pn < p/2 < pn+1, where pn is the n-th prime. We study the following question: with what probability does there exist a prime in the interval (p, 2pn+1)? After the strong definition of the probability with help of the Ramanujan primes ([11], [12])and the introducing pseudo-Ramanujan primes, we show, that if such probability P exists, then P ≥ 0.5. We also study a...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1990
ISSN: 0022-314X
DOI: 10.1016/0022-314x(90)90056-w