منابع مشابه
Primes with an Average Sum of Digits
The main goal of this paper is to provide asymptotic expansions for the numbers #{p 6 x : p prime, sq(p) = k} for k close to ((q − 1)/2) logq x, where sq(n) denotes the q-ary sum-of-digits function. The proof is based on a thorough analysis of exponential sums of the form ∑ p6x e(αsq(p)) (the sum is restricted to p prime), where we have to extend a recent result by the second two authors.
متن کاملPrescribing the Binary Digits of Primes
We present a new result on counting primes p < N = 2 for which r (arbitrarily placed) digits in the binary expansion of p are specified. Compared with earlier work of Harman and Katai, the restriction on r is relaxed to r < c ( n log n )4/7 . This condition results from the estimates of Gallagher and Iwaniec on zero-free regions of L-functions with ‘powerful’ conductor. (0). Summary This work i...
متن کاملCounting Primes whose Sum of Digits is Prime
Motivated by recent work of Drmota, Mauduit and Rivat, we discuss the possibility of counting the number of primes up to x whose sum of digits is also prime. We show that, although this is not possible unless we assume a hypothesis on the distribution of primes stronger than what is implied by the Riemann hypothesis, we can establish a Mertens-type result. That is, we obtain a formula for the n...
متن کاملThe sum of digits of primes in Z[i]
We study the distribution of the complex sum-of-digits function sq with basis q = −a ± i, a ∈ Z+ for Gaussian primes p. Inspired by a recent result of Mauduit and Rivat [16] for the real sum-of-digits function, we here get uniform distribution modulo 1 of the sequence (αsq(p)) provided α ∈ R \Q and q is prime with a ≥ 28. We also determine the order of magnitude of the number of Gaussian primes...
متن کاملImplementing Adams Methods with Preassigned Stepsize Ratios
Runge-Kutta and Adams methods are the most popular codes to solve numerically nonstiff ODEs. The Adams methods are useful to reduce the number of function calls, but they usually require more CPU time than the Runge-Kutta methods. In this work we develop a numerical study of a variable step length Adams implementation, which can only take preassigned step-size ratios. Our aim is the reduction o...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2008
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa133-2-5