On a function due to S. Chowla
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,...
متن کاملDedicated to Professor S. Chowla on the Occasion of His 70th Birthday
wherep is a prime withp = 1 (mod k). The evaluation of G, was first achieved by Gauss. The sums Gk for k = 3,4, 5, and 6 have also been studied. It is known that G, is a root of a certain irreducible cubic polynomial. Except for a sign ambiguity, the value of G4 is known. See Hasse’s text [24, pp. 478-4941 for a detailed treatment of G, and G, , and a brief account of G, . For an account of G, ...
متن کاملSome Remarks on a Problem of Chowla
Cette conjecture fut par la suite prouvée et généralisée par Baker, Birch et Wirsing. Dans leur article conjoint, Baker, Birch et Wirsing affirment que Chowla a aussi résolu le cas particulier que ce dernier a énoncé, mais ne donnent aucune indication sur le genre de démonstration effectuée. En nous basant sur certains articles préalablement écrits par Chowla, nous essayons de reconstruire ce q...
متن کاملil 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,...
متن کاملcompactifications and function spaces on weighted semigruops
chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1973
ISSN: 0022-314X
DOI: 10.1016/0022-314x(73)90072-3