Large Sieve Inequality with Quadratic Amplitudes
نویسندگان
چکیده
منابع مشابه
The Large Sieve Inequality for Quadratic Polynomial Amplitudes
Basic examples of sparse sequences of integers are provided by the sequence of values of polynomials of degree ≥ 2 with integer coefficients. The present article is concerned with the case when polynomial is of degree 2. Indeed, in a recent note, Liangyi Zhao [4], showed, by an elegant application of the double large sieve inequality of Bombieri and Iwaniec, that one has the estimate given belo...
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The quadratic sieve algorithm was used to factor a 47-digit number into primes. A comparison with Wagstaff's results using the continued fraction early abort algorithm suggests that QS should be faster than CFEA when the number being factored exceeds 60 digits (plus or minus ten or more digits, depending on details of the hardware and software).
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i∈I aie(xf(i))| 2, where e(z) denotes e2πiz for any complex number z, X is a wellspaced set of real numbers, I is an interval of the integers , {ai}i∈I are complex numbers and f is real valued function on I such that f(I) is sparse, that is, the length of f(I) is much larger than the length of I . When f(I) is sparse , the duality argument that is used to establish the classical large sieve ine...
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L’accès aux articles de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://jtnb.cedram. org/legal/). Toute reproduction en tout ou partie cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction...
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AMS Subject Classi cation: 11A51, 11Y05.
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2006
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-006-0408-6