Available in electronic format
Available in print format
Mathematics of Computation
Journal of the American Mathematical Society
ISSN 1088-6842(e) ISSN 0025-5718(p)
     

Explicit upper bounds for exponential sums over primes

Author(s): Hedi Daboussi; Joël Rivat.
Journal: Math. Comp. 70 (2001), 431-447.
MSC (2000): Primary 11L07, 11L20
Posted: June 12, 2000
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

We give explicit upper bounds for linear trigonometric sums over primes.


References:

1.
J. CHEN, On the estimation of some trigonometrical sums and their application (Chinese), Scientia Sinica, 28 (1985), pp. 449-458. MR 87h:11078

2.
J. CHEN AND T. WANG, On the Goldbach problem (Chinese), Acta Mathematica Sinica, 32 (1989), No. 5, pp. 702-718. MR 91e:11108

3.
-, Estimation of linear trigonometric sums with primes (Chinese), Acta Mathematica Sinica, 37 (1994), No. 1, pp. 25-31. MR 95c:11102

4.
H. DABOUSSI, Effective estimates of exponential sums over primes, Analytic Number Theory, Vol. 1, Progr. Math., 138, Birkhäuser, Boston, 1996, pp. 231-244. MR 97i:11088

5.
P. DUSART, Autour de la fonction qui compte le nombre de nombres premiers, PhD thesis, Université de Limoges, 1998.

6.
P. D. T. A. ELLIOTT, Probabilistic Number Theory I, vol. 239 of Grundlehren der mathematichen Wissenschaften, Springer-Verlag, 1979. MR 82h:10002a

7.
H. L. MONTGOMERY AND R. C. VAUGHAN, The large sieve, Mathematika, 20 (1973), pp. 119-134. MR 51:10260

8.
J. B. ROSSER AND L. SCHOENFELD, Approximate formulas for some functions of prime numbers, Illinois Journal of Mathematics, 6 (1962), pp. 64-94. MR 25:1139

9.
-, Sharper bounds for the Chebyshev functions $\theta(x)$ and $\psi(x)$, Mathematics of Computation, 29 (1975), pp. 243-269. MR 56:15581a

10.
H. SIEBERT, Montgomery's weighted sieve for dimension two, Monatshefte für Mathematik, 82 (1976), pp. 327-336. MR 54:12690

11.
R. C. VAUGHAN, An elementary method in prime number theory, Acta Arithmetica, 37 (1980), pp. 111-115. MR 82c:10055

12.
I. M. VINOGRADOV, Representation of an odd number as the sum of three primes, Dokl. Akad. Nauk SSSR, 15 (1937), pp. 291-294.

13.
-, The method of Trigonometrical Sums in the Theory of Numbers, translated from the Russian, revised and annotated by K.F. Roth and A. Davenport, Interscience, London, 1954. MR 15:941b


Similar Articles:

Retrieve articles in Mathematics of Computation with MSC (2000): 11L07, 11L20

Retrieve articles in all Journals with MSC (2000): 11L07, 11L20


Additional Information:

Hedi Daboussi
Affiliation: Faculté de Mathématiques et d'Informatique, 33 rue Saint-Leu, 80039 Amiens, France
Address at time of publication: UMR CNRS 8752, Mathématiques, Université Paris-Sud, 91405 Orsay Cedex, France
Email: daboussi@math.u-psud.fr

Joël Rivat
Affiliation: Institut Girard Desargues, CNRS UPRES-A 5028, Université Lyon I, 43, boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
Address at time of publication: Institut Elie Cartan, Université Henri Poincaré, B.P. 239, 54506 Vandoeuvre cedex, France
Email: rivat@iecn.u-nancy.fr

DOI: 10.1090/S0025-5718-00-01280-1
PII: S 0025-5718(00)01280-1
Keywords: Prime numbers, exponential sums, sieves
Received by editor(s): November 3, 1998
Posted: June 12, 2000
Dedicated: Dedicated to the memory of Chen Jing Run
Copyright of article: Copyright 2000, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google