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Almost-primes represented by quadratic polynomials

100%

Lemke Oliver R.

Acta Arithmetica

2012

tom 151

nr 3

241-261

Multiplicative functions dictated by Artin symbols

100%

Lemke Oliver R.

Acta Arithmetica

2013

tom 161

nr 1

21-31

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.

Ograniczanie wyników

2 Acta Arithmetica

2 Lemke Oliver R.

1 2013

1 2012

Wyniki wyszukiwania

Almost-primes represented by quadratic polynomials

Multiplicative functions dictated by Artin symbols