Multiplicative functions dictated by Artin symbols

• Autorzy: Robert J. Lemke Oliver
• Języki publikacji: EN

Abstrakty

EN

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 $𝓢_K$ of completely multiplicative functions whose values are dictated by Artin symbols, and we show that the only functions in $𝓢_K$ whose partial sums exhibit greater than expected cancellation are Dirichlet characters.

Kategorie tematyczne

• 11R42: Zeta functions and L -functions of number fields
• 11M41: Other Dirichlet series and zeta functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 1
• Strony: 21-31

Daty

wydano

2013

Twórcy

autor

Robert J. Lemke Oliver

• Department of Mathematics and Computer Science, Emory University, 400 Dowman Dr., Atlanta, GA 30322, U.S.A.
• Department of Mathematics, Stanford University, Building 380, Stanford, CA 94305, U.S.A.

Identyfikatory

DOI

10.4064/aa161-1-2