Ratios of Artin L-functions

@article{Hochfilzer2019RatiosOA,
  title={Ratios of Artin L-functions},
  author={Leonhard Hochfilzer and Thomas D Oliver},
  journal={arXiv: Number Theory},
  year={2019}
}
1 Citations

References

SHOWING 1-10 OF 22 REFERENCES
Poles of Artin L-functions and the strong Artin conjecture
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
L-FUNCTIONS AS DISTRIBUTIONS
We define an axiomatic class of L-functions extending the Selberg class. We show in particular that one can recast the traditional conditions of an Euler product, analytic continuation and functional
Linear independence of L-functions
Abstract We prove the linear independence of the L-functions, and of their derivatives of any order, in a large class 𝒞 defined axiomatically. Such a class contains in particular the Selberg class
Weil’s converse theorem for Maass forms and cancellation of zeros
We first prove a new converse theorem for Dirichlet series of Maass type which does not assume an Euler product. The underlying idea is a geometric generalisation of Weil's classical argument. By
Simple zeros of automorphic $L$ -functions
We prove that the complete $L$ -function associated to any cuspidal automorphic representation of $\operatorname{GL}_{2}(\mathbb{A}_{\mathbb{Q}})$ has infinitely many simple zeros.
Weil's converse theorem with poles
We prove a generalization of the classical converse theorem of Weil, allowing the twists by non-trivial Dirichlet characters to have arbitrary poles.
Algebraic Number Theory
I: Algebraic Integers.- II: The Theory of Valuations.- III: Riemann-Roch Theory.- IV: Abstract Class Field Theory.- V: Local Class Field Theory.- VI: Global Class Field Theory.- VII: Zeta Functions
Analytic Number Theory
Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of $L$-functions Elementary sieve methods Bilinear forms and the large
An introduction to the Langlands program
Preface.- E. Kowalski - Elementary Theory of L-Functions I.- E. Kowalski - Elementary Theory of L-Functions II.- E. Kowalski - Classical Automorphic Forms.- E. DeShalit - Artin L-Functions.- E.
A Comparison of Zeros of $L$–functions
In this paper we examine the following question: Given two different Dirichlet series D1(s) and D2(s) which extend to meromorphic functions L1(s) and L2(s) on the complex plane C and which satisfy
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