THE AUTOCORRELATION OF THE MOBIUS FUNCTION AND CHOWLA'S CONJECTURE FOR THE RATIONAL FUNCTION FIELD
نویسندگان
چکیده
منابع مشابه
The autocorrelation of the Möbius function and Chowla ’ s conjecture for the rational function field in
Let Fq be a finite field of q elements, and let Fq[x] be the polynomial ring over Fq. The Möbius function of a nonzero polynomial F ∈ Fq[x] is defined to be μ(F) = (−1)r if F = cP1 · · ·Pr with 0 = c ∈ Fq and P1, . . . , Pr are distinct monic irreducible polynomials, and μ(F) = 0 otherwise. Let Mn ⊂ Fq[x] be the set of monic polynomials of degree n over Fq, which is of size #Mn = qn. For r > 0,...
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We prove a function field version of Chowla’s conjecture on the autocorrelation of the Möbius function in the limit of a large finite field.
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Let Fq be a finite field of q elements, and let Fq[x] be the polynomial ring over Fq. The Möbius function of a nonzero polynomial F ∈ Fq[x] is defined to be μ(F) = (−1)r if F = cP1 · · ·Pr with 0 = c ∈ Fq and P1, . . . , Pr are distinct monic irreducible polynomials, and μ(F) = 0 otherwise. Let Mn ⊂ Fq[x] be the set of monic polynomials of degree n over Fq, which is of size #Mn = qn. For r > 0,...
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We prove a function field version of Chowla's conjecture on the autocorrelation of the Möbius function in the limit of a large finite field of characteristic 2, extending previous work in odd characteristic.
متن کاملil The autocorrelation of the Möbius function and Chowla ’ s conjecture for the rational function field in characteristic
Let Fq be a finite field of q elements, and let Fq[x] be the polynomial ring over Fq. The Möbius function of a nonzero polynomial F ∈ Fq[x] is defined to be μ(F) = (−1)r if F = cP1 · · ·Pr with 0 = c ∈ Fq and P1, . . . , Pr are distinct monic irreducible polynomials, and μ(F) = 0 otherwise. Let Mn ⊂ Fq[x] be the set of monic polynomials of degree n over Fq, which is of size #Mn = qn. For r > 0,...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2013
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/has047