Biases in the Shanks - Rényi Prime Number Race
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چکیده
منابع مشابه
1 N ov 1 99 9 BIASES IN THE SHANKS – RÉNYI PRIME NUMBERS RACE
Rubinstein and Sarnak investigated systems of inequalities of the form π(x; q, a 1) > · · · > π(x; q, a r), where π(x; q, a) denotes the number of primes up to x that are congruent to a mod q. They showed, under standard hypotheses on the zeros of Dirichlet L-functions mod q, that the set of positive real numbers x for which these inequalities hold has positive (logarithmic) density δ q;a 1 ,.....
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The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced a...
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In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X +nY , n ≥ 1. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n = 2. In this paper, we prove that in fact this constant is unbounded as one runs throu...
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عنوان ژورنال:
- Experimental Mathematics
دوره 9 شماره
صفحات -
تاریخ انتشار 2000