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• # Artykuł - szczegóły

## Acta Arithmetica

2013 | 161 | 1 | 21-31

## Multiplicative functions dictated by Artin symbols

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.

21-31

wydano
2013

### Twórcy

• 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.