On the order of

E. Bombieri; H. Iwaniec

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1986)

  • Volume: 13, Issue: 3, page 449-472
  • ISSN: 0391-173X

How to cite

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Bombieri, E., and Iwaniec, H.. "On the order of $\zeta (\frac{1}{2} + it)$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 13.3 (1986): 449-472. <http://eudml.org/doc/83987>.

@article{Bombieri1986,
author = {Bombieri, E., Iwaniec, H.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Riemann zeta-function; critical strip; exponential sum; average of short sums; Gauss sums; large sieve; mean value theorem},
language = {eng},
number = {3},
pages = {449-472},
publisher = {Scuola normale superiore},
title = {On the order of $\zeta (\frac\{1\}\{2\} + it)$},
url = {http://eudml.org/doc/83987},
volume = {13},
year = {1986},
}

TY - JOUR
AU - Bombieri, E.
AU - Iwaniec, H.
TI - On the order of $\zeta (\frac{1}{2} + it)$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1986
PB - Scuola normale superiore
VL - 13
IS - 3
SP - 449
EP - 472
LA - eng
KW - Riemann zeta-function; critical strip; exponential sum; average of short sums; Gauss sums; large sieve; mean value theorem
UR - http://eudml.org/doc/83987
ER -

References

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  1. [1] E. Bombieri - H. Iwaniec, Some mean-value theorems jor exponential sums, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 13, no. 3 (1986), pp. 473-486. Zbl0615.10046MR881102
  2. [2] J.-M. Deshouillers - H. Iwaniec, Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math., 70 (1982), pp. 219-288. Zbl0502.10021MR684172
  3. [3] J.B. Friedlander - H. Iwaniec, On the distribution of the sequence n2θ(mod 1), to appear in the Canadian J. Math. Zbl0625.10029
  4. [4] S.W. Graham - G. Kolesnik, One and two dimensional exponential sums, preprint 1984 (to be published in the Proceedings from the Conference on Number Theory Held at the OSU in July 1984). Zbl0626.10034MR1018377
  5. [5] G.H. Hardy, On certain definite integrals considered by Airy and by Stokes, Quart. J. Math., 44 (1910), pp. 226-240. Zbl41.0322.01JFM41.0322.01
  6. [6] G. Kolesnik, On the method of exponent pairs, Acta Arith., 55 (1985), pp.115-143. Zbl0571.10036MR797257
  7. [7] E. Phillips, The zeta-function of Riemann: further developments of van der Corput's method, Quart. J. Math., 4 (1933), pp. 209-225. Zbl0007.29801JFM59.0204.01
  8. [8] R.A. Rankin, Van der Corput's method and the theory of exponent pairs, Quart. J. Math., 6 (1955), pp. 147-153. Zbl0065.27802MR72170
  9. [9] E.C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford1951. Zbl0042.07901MR46485
  10. [10] J.D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc., 42 (2) (1985), pp. 183-216. Zbl0575.42003MR776471

Citations in EuDML Documents

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  1. Ekkehard Krätzel, Werner Nowak, László Tóth, On certain arithmetic functions involving the greatest common divisor
  2. E. Bombieri, H. Iwaniec, Some mean-value theorems for exponential sums
  3. Xiaodong Cao, Wenguang Zhai, On the distribution of modulo one
  4. Hong-Quan Liu, The greatest prime factor of the integers in an interval
  5. Xiaodong Cao, Wenguang Zhai, Multiple exponential sums with monomials
  6. D. I. Tolev, On a theorem of Bombieri-Vinogradov type for prime numbers from a thin set
  7. Nigel Watt, An elementary treatment of a general diophantine problem
  8. Xiaodong Cao, Wenguang Zhai, The distribution of square-free numbers of the form
  9. J. Wu, Nombres 𝓑-libres dans les petits intervalles
  10. Hong-Quan Liu, The number of squarefull numbers in an interval

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