$L$ functions for the group $G_2$
نویسندگان
چکیده
منابع مشابه
L Functions for the Group
The method of L functions is one of the major methods for analyzing automorphic forms. For example, the Hecke Converse Theorem gives an equivalence via the Mellin transform between holomorphic modular forms on the upper half plane and certain L functions associated to Dirichlet series, which have analytic continuation and functional equation. The classical theory of automorphic forms on the gro...
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Let $G$ be a finite group. The prime graph of $G$ is a graph $Gamma(G)$ with vertex set $pi(G)$, the set of all prime divisors of $|G|$, and two distinct vertices $p$ and $q$ are adjacent by an edge if $G$ has an element of order $pq$. In this paper we prove that if $Gamma(G)=Gamma(G_2(5))$, then $G$ has a normal subgroup $N$ such that $pi(N)subseteq{2,3,5}$ and $G/Nequiv G_2(5)$.
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Let K be a totally imaginary quadratic extension of a totally real number field F , and assume that F has narrow ideal class number 1. Let χ be a character of the ideal class group CL(K) of K, and let LK(χ, s) be its associated L–function. In this paper we prove that for all > 0, #{χ ∈ CL(K)∧ : LK(χ, 1 2 ) 6= 0} ,F d 1 100− K as the absolute discriminant dK →∞.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1990
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1990-15942-7