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## References

SHOWING 1-10 OF 22 REFERENCES

Poles of Artin L-functions and the strong Artin conjecture

- Mathematics
- 2003

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

- Mathematics
- 2015

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

- Mathematics
- 2006

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

- Mathematics
- 2018

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

- MathematicsCompositio Mathematica
- 2019

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

- Mathematics
- 2014

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

- Mathematics
- 1999

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

- Mathematics
- 2004

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

- Mathematics
- 2004

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

- Mathematics
- 1999

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…