• Corpus ID: 117428676

Multiplicity one for $L$-functions and applications

@article{Farmer2013MultiplicityOF,
  title={Multiplicity one for \$L\$-functions and applications},
  author={David W. Farmer and Ameya Pitale and Nathan C. Ryan and Ralf Schmidt},
  journal={arXiv: Number Theory},
  year={2013}
}
We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients satisfy a partial Ramanujan bound and do not differ by too much. Additionally, we prove a number of multiplicity one type results for the number-theoretic objects attached to $L$-functions. These results follow from our main result about $L$-functions. 

References

SHOWING 1-10 OF 29 REFERENCES

On the holomorphy of exterior-square L-functions

In this paper, we show that the twisted partial exterior-square $L$-function has a meromorphic continuation to the whole complex plane with only two possible simple poles at $s=1$ and $s=0$. We do

Multiplicity one Theorems

In the local, characteristic 0, non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by

Strong multiplicity one for the Selberg class

Refinement of strong multiplicity one for automorphic representations of GL(n)

We state a qualitative form of strong multiplicity one for GL 1 . We derive refinements of strong multiplicity one for automorphic representations arising from Eisenstein series associated to a Borel

A relation between multiplicity one and Böcherer’s conjecture

We show that a weak form of the generalized Böcherer conjecture implies multiplicity one for Siegel cusp forms of degree 2.

EULER PRODUCTS CORRESPONDING TO SIEGEL MODULAR FORMS OF GENUS 2

In this article we construct a theory of Dirichlet series with Euler product expansions corresponding to analytic automorphic forms for the integral symplectic group in genus 2; in Chapter 2 we

Strong Multiplicity One for the Selberg Class

Abstract We investigate the problem of determining elements in the Selberg class by means of their Dirichlet series coefficients at primes.

Transfer of Siegel Cusp Forms of Degree 2

Introduction Notation Distinguished vectors in local representations Global L-functions for GSp? X GL? The pullback formula Holomorphy of global L-functions for GSp? X GL? Applications Bibliography

Notes on the Generalized Ramanujan Conjectures

1. GLn Ramanujan's original conjecture is concerned with the estimation of Fourier coe! cients of the weight 12 holomorphic cusp form " for SL(2,Z) on the upper half plane H. The conjecture may be

The role of the Ramanujan conjecture in analytic number theory

We discuss progress towards the Ramanujan conjecture for the group GLn and its relation to various other topics in analytic number theory.