Exponential sums with multiplicative coefficients and applications-Reference-Cited by-同舟云学术

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Exponential sums with multiplicative coefficients and applications

Published:2022-07-25 Issue:10 Volume:375 Page:6875-6901
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

de la Bretèche Régis,Granville Andrew

Abstract

We show that if an exponential sum with multiplicative coefficients is large then the associated multiplicative function is “pretentious”. This leads to applications in the circle method, and a natural interpretation of the local-global principle.

Funder

Natural Sciences and Engineering Research Council of Canada

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/tran/2022-375-10/S0002-9947-2022-08625-6/tran8625_AM.pdf

Reference24 articles.

1. On exponential sums with multiplicative coefficients. II;Bachman, Gennady;Acta Arith.,2003

2. Sommes d’exponentielles et entiers sans grand facteur premier;de la Bretèche, R.;Proc. London Math. Soc. (3),1998

3. Sommes sans grand facteur premier;de la Bretèche, R.;Acta Arith.,1999

4. Binary additive problems and the circle method, multiplicative sequences and convergent sieves;Brüdern, Jörg,2009

5. Exponential sums modulo prime powers;Cochrane, Todd;Acta Arith.,2002

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