Selberg's Conjectures and Artin $L$-functions
نویسندگان
چکیده
منابع مشابه
Selberg's Conjectures and Artin L-functions
In its comprehensive form, an identity between an automorphic L-function and a "motivic" L-function is called a reciprocity law. The celebrated Artin reciprocity law is perhaps the fundamental example. The conjecture of ShimuraTaniyama that every elliptic curve over Q is "modular" is certainly the most intriguing reciprocity conjecture of our time. The "Himalayan peaks" that hold the secrets of...
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We show that if the L-function of an irreducible 2-dimensional complex Galois representation over Q is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a single representation implies the corresponding strong Artin conjecture. Introduction Let ρ : Gal(Q/Q) → GLn(C) be an irreducible continuous representation of the absolute Galois group of Q. Brauer [2]...
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Some identities between unitary minimal Virasoro characters at levels m = 3, 4, 5 are shown to arise as a consequence of relations between Artin L-functions of different quadratic fields. The definitions and concepts of number theory necessary to present the theta function identities which can be derived from these relations are introduced. A new infinite family of identities between Virasoro c...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1994
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1994-00479-3