On oscillations in the additive divisor problem, 1

Bogdan Szydło

Acta Arithmetica (1994)

  • Volume: 66, Issue: 1, page 63-69
  • ISSN: 0065-1036

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Bogdan Szydło. "On oscillations in the additive divisor problem, 1." Acta Arithmetica 66.1 (1994): 63-69. <http://eudml.org/doc/206592>.

@article{BogdanSzydło1994,
author = {Bogdan Szydło},
journal = {Acta Arithmetica},
keywords = {additive divisor problem; Omega theorem; error term},
language = {eng},
number = {1},
pages = {63-69},
title = {On oscillations in the additive divisor problem, 1},
url = {http://eudml.org/doc/206592},
volume = {66},
year = {1994},
}

TY - JOUR
AU - Bogdan Szydło
TI - On oscillations in the additive divisor problem, 1
JO - Acta Arithmetica
PY - 1994
VL - 66
IS - 1
SP - 63
EP - 69
LA - eng
KW - additive divisor problem; Omega theorem; error term
UR - http://eudml.org/doc/206592
ER -

References

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  1. [1] R. J. Anderson and H. M. Stark, Oscillation theorems, in: Lecture Notes in Math. 899, Springer, 1981, 79-106. 
  2. [2] J.-M. Deshouillers and H. Iwaniec, Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math. 70 (1982), 219-288. 
  3. [3] J.-M. Deshouillers and H. Iwaniec, Additive divisor problem, J. London Math. Soc. (2) 26 (1982), 1-14. 
  4. [4] A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, II, McGraw-Hill, 1953. Zbl0052.29502
  5. [5] M. Jutila, The additive divisor problem and exponential sums, in: Third Conference of the Canadian Number Theory Association, Kingston 1991, Clarendon Press, Oxford, 1993, 113-135. 
  6. [6] T. Kubota, Elementary Theory of Eisenstein Series, Wiley, New York, 1973. Zbl0268.10012
  7. [7] N. V. Kuznetsov, Petersson's conjecture for cusp forms of weight zero and Linnik's conjecture. Sums of Kloosterman sums, Math. USSR-Sb. 39 (1981), 299-342. Zbl0461.10017
  8. [8] N. V. Kuznetsov, Convolutions of the Fourier coefficients of the Eisenstein-Maass series, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 134 (1983), 43-84 (in Russian). Zbl0496.10013
  9. [9] E. Landau, Über einen Satz von Tschebyschef, Math. Ann. 61 (1905), 527-550. 
  10. [10] Y. Motohashi, The binary additive divisor problem, Ann. Sci. École Norm. Sup., to appear. Zbl0819.11038
  11. [11] Y. Motohashi, Spectral mean values of Maass waveform L-functions, J. Number Theory 42 (1992), 258-284. Zbl0759.11026
  12. [12] N. V. Proskurin, Summation formulas for generalized Kloosterman sums, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 82 (1979), 103-135 (in Russian). 
  13. [13] L. A. Takhtajan and A. I. Vinogradov, The Gauss-Hasse hypothesis on real quadratic fields with class number one, J. Reine Angew. Math. 335 (1982), 40-87. 
  14. [14] L. A. Takhtajan and A. I. Vinogradov, The zeta-function of the additive divisor problem and the spectral decomposition of the automorphic Laplacian, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 134 (1984), 84-116 (in Russian). Zbl0536.10025
  15. [15] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed. revised by D. R. Heath-Brown, Clarendon Press, Oxford, 1986. Zbl0601.10026

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