Multiplicative functions dictated by Artin symbols

Robert J. Lemke Oliver

Acta Arithmetica (2013)

  • Volume: 161, Issue: 1, page 21-31
  • ISSN: 0065-1036

Abstract

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Granville and Soundararajan have recently suggested that a general study of multiplicative functions could form the basis of analytic number theory without zeros of L-functions; this is the so-called pretentious view of analytic number theory. Here we study multiplicative functions which arise from the arithmetic of number fields. For each finite Galois extension K/ℚ, we construct a natural class K of completely multiplicative functions whose values are dictated by Artin symbols, and we show that the only functions in K whose partial sums exhibit greater than expected cancellation are Dirichlet characters.

How to cite

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Robert J. Lemke Oliver. "Multiplicative functions dictated by Artin symbols." Acta Arithmetica 161.1 (2013): 21-31. <http://eudml.org/doc/279161>.

@article{RobertJ2013,
abstract = {Granville and Soundararajan have recently suggested that a general study of multiplicative functions could form the basis of analytic number theory without zeros of L-functions; this is the so-called pretentious view of analytic number theory. Here we study multiplicative functions which arise from the arithmetic of number fields. For each finite Galois extension K/ℚ, we construct a natural class $_K$ of completely multiplicative functions whose values are dictated by Artin symbols, and we show that the only functions in $_K$ whose partial sums exhibit greater than expected cancellation are Dirichlet characters.},
author = {Robert J. Lemke Oliver},
journal = {Acta Arithmetica},
keywords = {pretentiousness; Selberg class; Artin L-functions; Artin symbol},
language = {eng},
number = {1},
pages = {21-31},
title = {Multiplicative functions dictated by Artin symbols},
url = {http://eudml.org/doc/279161},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Robert J. Lemke Oliver
TI - Multiplicative functions dictated by Artin symbols
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 1
SP - 21
EP - 31
AB - Granville and Soundararajan have recently suggested that a general study of multiplicative functions could form the basis of analytic number theory without zeros of L-functions; this is the so-called pretentious view of analytic number theory. Here we study multiplicative functions which arise from the arithmetic of number fields. For each finite Galois extension K/ℚ, we construct a natural class $_K$ of completely multiplicative functions whose values are dictated by Artin symbols, and we show that the only functions in $_K$ whose partial sums exhibit greater than expected cancellation are Dirichlet characters.
LA - eng
KW - pretentiousness; Selberg class; Artin L-functions; Artin symbol
UR - http://eudml.org/doc/279161
ER -

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