Results 221 to 230 of about 27,028 (268)
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International Journal of Number Theory, 2005
We study some of the extremely strong statements that can be made about the distribution of primes assuming the (unlikely) existence of exceptional Dirichlet characters. We treat this in general and then apply the results to the particular cases of primes of the form a2 + b6 and of elliptic curves having prime discriminant.
Friedlander, J. B., Iwaniec, H.
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We study some of the extremely strong statements that can be made about the distribution of primes assuming the (unlikely) existence of exceptional Dirichlet characters. We treat this in general and then apply the results to the particular cases of primes of the form a2 + b6 and of elliptic curves having prime discriminant.
Friedlander, J. B., Iwaniec, H.
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Lithuanian Mathematical Journal, 2021
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Mathematika, 1965
The purpose of this paper is to give a new and improved version of Linnik's large sieve, with some applications. The large sieve has its roots in the Hardy-Littlewood method, and in its most general form it may be considered as an inequality which relates a singular series arising from an integral where S(α) is any exponential sum, to the integral ...
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The purpose of this paper is to give a new and improved version of Linnik's large sieve, with some applications. The large sieve has its roots in the Hardy-Littlewood method, and in its most general form it may be considered as an inequality which relates a singular series arising from an integral where S(α) is any exponential sum, to the integral ...
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Canadian Journal of Mathematics, 1987
Let v(n) denote the number of distinct prime factors of a natural number n. A classical theorem of Hardy and Ramanujan states that the normal order of v(n) is log log n. That is, given any , the number of natural numbers not exceeding x which fail to satisfy the inequality1is o(x) as x → ∞.
Murty, M. Ram, Saradha, N.
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Let v(n) denote the number of distinct prime factors of a natural number n. A classical theorem of Hardy and Ramanujan states that the normal order of v(n) is log log n. That is, given any , the number of natural numbers not exceeding x which fail to satisfy the inequality1is o(x) as x → ∞.
Murty, M. Ram, Saradha, N.
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Journal of Philosophical Logic, 1980
The validity of an entailment has nothing to do with whether or not the components are true, false, necessary, or impossible; it has to do solely with whether or not there is a necessary connection between antecedent and consequent. Hence it is a mistake (we feel) to try to build a sieve which will “strain out” entailments from the set of material or ...
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The validity of an entailment has nothing to do with whether or not the components are true, false, necessary, or impossible; it has to do solely with whether or not there is a necessary connection between antecedent and consequent. Hence it is a mistake (we feel) to try to build a sieve which will “strain out” entailments from the set of material or ...
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Science, 1998
The enzymes that load amino acids onto their respective tRNAs in preparation for protein synthesis must do so with high accuracy. Now a structure of the synthase for isoleucine reported by Nureki et al . in this issue shows how this is accomplished.
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The enzymes that load amino acids onto their respective tRNAs in preparation for protein synthesis must do so with high accuracy. Now a structure of the synthase for isoleucine reported by Nureki et al . in this issue shows how this is accomplished.
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Mathematics of Computation, 2015
We propose an efficient variant for the initialisation step of quadratic sieving, the sieving step of the quadratic sieve and its variants, which is also used in sieving-based algorithms for computing class groups of quadratic fields. As an application we computed the class groups of imaginary quadratic fields with 100-, 110-, 120-, and 130-digit ...
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We propose an efficient variant for the initialisation step of quadratic sieving, the sieving step of the quadratic sieve and its variants, which is also used in sieving-based algorithms for computing class groups of quadratic fields. As an application we computed the class groups of imaginary quadratic fields with 100-, 110-, 120-, and 130-digit ...
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Designs, Codes and Cryptography, 1999
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Shuhong Gao, Jason Howell
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Shuhong Gao, Jason Howell
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The British Journal of Radiology, 1952
In an endeavour to enlarge the scope of radiotherapy and to improve the results of treatment by a new method, it is imperative to state clearly some of the basic principles underlying the suggested procedure. It seems appropriate therefore to uphold certain fundamentals of radiobiology briefly and to scrutinise whether at any point our present-day ...
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In an endeavour to enlarge the scope of radiotherapy and to improve the results of treatment by a new method, it is imperative to state clearly some of the basic principles underlying the suggested procedure. It seems appropriate therefore to uphold certain fundamentals of radiobiology briefly and to scrutinise whether at any point our present-day ...
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