On a conjecture of S. Chowla and of S. Chowla and H. Walum, I
نویسندگان
چکیده
منابع مشابه
Chowla-selberg Formula and Colmez’s Conjecture
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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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Let p be a prime congruent to 1 modulo 4, and let t, u be rational integers such that (t + u √ p )/2 is the fundamental unit of the real quadratic field Q(√p ). The Ankeny-Artin-Chowla conjecture (AAC conjecture) asserts that p will not divide u. This is equivalent to the assertion that p will not divide B(p−1)/2, where Bn denotes the nth Bernoulli number. Although first published in 1952, this...
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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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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1985
ISSN: 0022-314X
DOI: 10.1016/0022-314x(85)90020-4