The mean values of Dirichlet L-functions at integer points and class numbers of cyclotomic fields
نویسندگان
چکیده
منابع مشابه
On the Mean Values of Dirichlet L-functions
Abstract. We study the 2k-th power moment of Dirichlet L-functions L(s, χ) at the centre of the critical strip (s = 1/2), where the average is over all primitive characters χ (mod q). We extend to this case the hybrid Euler-Hadamard product results of Gonek, Hughes and Keating for the Riemann zeta-function. This allows us to recover conjectures for the moments based on random matrix models, inc...
متن کاملClass Numbers of Cyclotomic Function Fields
Let q be a prime power and let Fq be the nite eld with q elements. For each polynomial Q(T) in FqT ], one could use the Carlitz module to construct an abelian extension of Fq(T), called a Carlitz cyclotomic extension. Carlitz cyclotomic extensions play a fundamental role in the study of abelian extensions of Fq(T), similar to the role played by cyclotomic number elds for abelian extensions of Q...
متن کاملExtreme values of Artin L-functions and class numbers
Assuming the GRH and Artin conjecture for Artin L-functions, we prove that there exists a totally real number field of any fixed degree (> 1) with an arbitrarily large discriminant whose normal closure has the full symmetric group as Galois group and whose class number is essentially as large as possible. One ingredient is an unconditional construction of totally real fields with small regulato...
متن کاملThe Mean-square of Dirichlet L-functions
where α and β are small complex numbers satisfying α, β ≪ 1/ log q. Ingham [Ing] considered an analogous moment for the Riemann zeta-function on the critical line with small shifts. Paley [Pal] considered the moment above for Dirichlet L-functions. Heath-Brown [HB] has computed a similar moment, but for all characters modulo q, in the case that α = β = 0. His result is Theorem 1 (HB). There are...
متن کاملClass numbers of real cyclotomic fields of prime conductor
The class numbers h+l of the real cyclotomic fields Q(ζl + ζ −1 l ) are notoriously hard to compute. Indeed, the number h+l is not known for a single prime l ≥ 71. In this paper we present a table of the orders of certain subgroups of the class groups of the real cyclotomic fields Q(ζl + ζ −1 l ) for the primes l < 10, 000. It is quite likely that these subgroups are in fact equal to the class ...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1994
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000004906