Three two-dimensional Weyl steps in the circle problem II. The logarithmic Riesz mean for a class of arithmetic functions

Ulrike M. A. Vorhauer

Acta Arithmetica (1999)

  • Volume: 91, Issue: 1, page 57-73
  • ISSN: 0065-1036

Abstract

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1. Summary. In Part II we study arithmetic functions whose Dirichlet series satisfy a rather general type of functional equation. For the logarithmic Riesz mean of these functions we give a representation involving finite trigonometric sums. An essential tool here is the saddle point method. Estimation of the exponential sums in the special case of the circle problem will be the topic of Part III.

How to cite

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Ulrike M. A. Vorhauer. "Three two-dimensional Weyl steps in the circle problem II. The logarithmic Riesz mean for a class of arithmetic functions." Acta Arithmetica 91.1 (1999): 57-73. <http://eudml.org/doc/207339>.

@article{UlrikeM1999,
abstract = {1. Summary. In Part II we study arithmetic functions whose Dirichlet series satisfy a rather general type of functional equation. For the logarithmic Riesz mean of these functions we give a representation involving finite trigonometric sums. An essential tool here is the saddle point method. Estimation of the exponential sums in the special case of the circle problem will be the topic of Part III.},
author = {Ulrike M. A. Vorhauer},
journal = {Acta Arithmetica},
keywords = {circle problem; logarithmic Riesz mean; asymptotic representation; finite trigonometric sums},
language = {eng},
number = {1},
pages = {57-73},
title = {Three two-dimensional Weyl steps in the circle problem II. The logarithmic Riesz mean for a class of arithmetic functions},
url = {http://eudml.org/doc/207339},
volume = {91},
year = {1999},
}

TY - JOUR
AU - Ulrike M. A. Vorhauer
TI - Three two-dimensional Weyl steps in the circle problem II. The logarithmic Riesz mean for a class of arithmetic functions
JO - Acta Arithmetica
PY - 1999
VL - 91
IS - 1
SP - 57
EP - 73
AB - 1. Summary. In Part II we study arithmetic functions whose Dirichlet series satisfy a rather general type of functional equation. For the logarithmic Riesz mean of these functions we give a representation involving finite trigonometric sums. An essential tool here is the saddle point method. Estimation of the exponential sums in the special case of the circle problem will be the topic of Part III.
LA - eng
KW - circle problem; logarithmic Riesz mean; asymptotic representation; finite trigonometric sums
UR - http://eudml.org/doc/207339
ER -

References

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  12. [12] H.-E. Richert, Beiträge zur Summierbarkeit Dirichletscher Reihen mit Anwendungen auf die Zahlentheorie, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. IIa (1956), 77-125. Zbl0071.28601
  13. [13] E. C. Titchmarsh, The Theory of Functions, 2nd ed., 1939, corrected reprint 1975, Oxford Univ. Press, London. Zbl0022.14602
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