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Exponential sums over primes and the prime twin problem

Acta Mathematica Hungarica
Volume/Issue:
Volume 131: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-010-0015-9
Author: Yvonne Buttkewitz

References [1] Daboussi , H. 1996 Effective estimates of exponential sums over primes Berndt , B. C. (eds.) et al. Analytic

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Higher order derivative tests for exponential sums incorporating the Discrete Hardy–Littlewood method

Acta Mathematica Hungarica
Volume/Issue:
Volume 134: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-011-0140-0
Author: Werner Georg Nowak

. [2] Graham , S. W. , Kolesnik , G. 1991 Van der Corput’s method of exponential sums University Press Cambridge 10.1017/CBO9780511661976 . [3] Huxley , M. N

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Exponential sums and prime divisors of sparse integers

Periodica Mathematica Hungarica
Volume/Issue:
Volume 57: Issue 1
DOI:
https://doi.org/10.1007/s10998-008-7093-3
Author: Igor Shparlinski

Abstract  

We obtain a new lower bound on the number of prime divisors of integers whose g-ary expansion contains a fixed number of nonzero digits.

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On the Exponential sum over r-Free Integers

Acta Mathematica Hungarica
Volume/Issue:
Volume 90: Issue 3
DOI:
https://doi.org/10.1023/a:1006754512257
Authors: A. Balog and I. Ruzsa

Abstract  

We determine, up to a constant factor, the L 1 mean of the exponential sum formed with the r-free integers. This improves earlier results of Brdern, Granville, Perelli, Vaughan and Wooley. As an application, we improve the known bound for the L 1 norm of the exponential sum defined with the Mbius function.

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An explicit formula for the fourth moment of certain exponential sums

Acta Mathematica Hungarica
Volume/Issue:
Volume 130: Issue 3
DOI:
https://doi.org/10.1007/s10474-010-0043-5
Authors: C. Calderón, M. J. de Velasco, and M. J. Zarate

. [3] Davenport , H. 1933 On certain exponential sums, I Reine Angew. Math. 169 158 – 176 . [4

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Weighted exponential sums and discrepancy

Acta Mathematica Hungarica
Volume/Issue:
Volume 54: Issue 1-2
DOI:
https://doi.org/10.1007/bf01950713
Authors: J. Horbowicz and H. Niederreiter
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Exponential sums with multiplicative coefficients

Acta Mathematica Hungarica
Volume/Issue:
Volume 54: Issue 3-4
DOI:
https://doi.org/10.1007/bf01952056
Authors: K. Indlekofer and I. Kátai
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Exponential sums over primes in short intervals

Acta Mathematica Hungarica
Volume/Issue:
Volume 48: Issue 1-2
DOI:
https://doi.org/10.1007/bf01949067
Authors: A. Balog and A. Perelli
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On exponential sums studied by Indlekofer and Kátai

Acta Mathematica Hungarica
Volume/Issue:
Volume 124: Issue 3
DOI:
https://doi.org/10.1007/s10474-009-8192-0
Author: G. Harman

Abstract  

We continue the study of sums of the form

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sum\limits_{m_j p \leqq x} {Y_{mj} X_p e(\alpha m_j p)} ,$$ \end{document}
begun by Indlekofer and Kátai. Here |Y n|,|X p| ≦ 1 and α is irrational. We prove one conjecture of Kátai, disprove another by both authors, and give what may be a close to best possible result valid for all irrational α.

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Exponential Sums for O+(2n,q) and Their Applications

Acta Mathematica Hungarica
Volume/Issue:
Volume 91: Issue 1-2
DOI:
https://doi.org/10.1023/a:1010634927604
Author: D. Kim
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