Topics in Multiplicative Number Theory

Montgomery, Hugh L.

doi:10.1007/bfb0060851

Cited by 514 publications

(386 citation statements)

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“…To handle the third term in (9) we use the zero density estimate The contribution of the third term in (9) to S n is therefore However the bound (14) shows that…”

Section: E Tfm(j?t)ro(iim")j(r)j(r')(mmentioning

confidence: 99%

Integers represented as a sum of primes and powers of two

Heath‐Brown¹,

Puchta²

2002

Asian Journal of Mathematics

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“…To handle the third term in (9) we use the zero density estimate The contribution of the third term in (9) to S n is therefore However the bound (14) shows that…”

Section: E Tfm(j?t)ro(iim")j(r)j(r')(mmentioning

confidence: 99%

Integers represented as a sum of primes and powers of two

Heath‐Brown¹,

Puchta²

2002

Asian Journal of Mathematics

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“…In [9], we explored numerically as well as theoretically the distribution of the eigenvalues of the hermitian form as "the large sieve" and we refer the reader to [7] and [1] for more details on this subject. Let us assume that…”

Section: Introductionmentioning

confidence: 99%

Eigenvalues in the large sieve inequality, II

Ramaré¹

2010

J. Théor. Nombres Bordeaux

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“…Graham and Ringrose [ 18] have shown that the least quadratic nonresidue modulo a prime p is infinitely often Q(logp log log log/? ), and Montgomery [31] gave a bound of f2(log/?loglog/?) assuming the ERH.…”

Section: Introductionmentioning

confidence: 99%

Explicit Bounds for Primality Testing and Related Problems

Bach¹

1990

Mathematics of Computation

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Abstract.Many number-theoretic algorithms rely on a result of Ankeny, which states that if the Extended Riemann Hypothesis (ERH) is true, any nontrivial multiplicative subgroup of the integers modulo m omits a number that is 0(log m). This has been generalized by Lagañas. Montgomery, and Odlyzko to give a similar bound for the least prime ideal that does not split completely in an abelian extension of number fields. This paper gives a different proof of this theorem, in which explicit constants are supplied. The bounds imply that if the ERH holds, a composite number m has a witness for its compositeness (in the sense of Miller or Solovay-Strassen) that is at most 2 log m .

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Topics in Multiplicative Number Theory

Cited by 514 publications

References 0 publications

Integers represented as a sum of primes and powers of two

Integers represented as a sum of primes and powers of two

Eigenvalues in the large sieve inequality, II

Explicit Bounds for Primality Testing and Related Problems

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