# Strong Multiplicity One for the Selberg Class

@article{Soundararajan2004StrongMO, title={Strong Multiplicity One for the Selberg Class}, author={Kannan Soundararajan}, journal={Canadian Mathematical Bulletin}, year={2004}, volume={47}, pages={468 - 474} }

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

## 11 Citations

### Strong multiplicity one for the Selberg class

- MathematicsMathematika
- 2021

We study the problem of determining elements of the Selberg class by information on the coefficents of the Dirichlet series at the squares of primes, or information about the zeroes of the functions.

### Distinguishing L-functions by joint universality

- MathematicsLithuanian Mathematical Journal
- 2021

In this note, we present results for distinguishing L -functions by their multisets of zeros and unique factorizations in an axiomatic setting; our tools stem from universality theory.

### On a generalization of the Euler totient function

- MathematicsMonatshefte für Mathematik
- 2012

For a general polynomial Euler product F(s) we define the associated Euler totient function φ(n, F) and study its asymptotic properties. We prove that for F(s) belonging to certain subclass of the…

### A refinement of strong multiplicity one for spectra of hyperbolic manifolds

- Mathematics
- 2011

Let $\calM_1$ and $\calM_2$ denote two compact hyperbolic manifolds. Assume that the multiplicities of eigenvalues of the Laplacian acting on $L^2(\calM_1)$ and $L^2(\calM_2)$ (respectively,…

### Analytic monoids and factorization problems

- Mathematics
- 2017

The main goal of this paper is to initiate study of analytic monoids as a general framework for quantitative theory of factorization. So far the latter subject was developed either in concrete…

### N T ] 1 9 Ju l 2 02 1 lADIC IMAGES OF GALOIS FOR ELLIPTIC CURVES OVER Q

- Mathematics
- 2021

We discuss the l-adic case of Mazur’s “Program B” over Q, the problem of classifying the possible images of l-adic Galois representations attached to elliptic curves E over Q, equivalently,…

### $\ell $ -adic images of Galois for elliptic curves over $\mathbb {Q}$ (and an appendix with John Voight)

- MathematicsForum of Mathematics, Sigma
- 2022

Abstract We discuss the
$\ell $
-adic case of Mazur’s ‘Program B’ over
$\mathbb {Q}$
: the problem of classifying the possible images of
$\ell $
-adic Galois representations attached to…

### A database of genus-2 curves over the rational numbers

- MathematicsLMS Journal of Computation and Mathematics
- 2016

<jats:p>We describe the construction of a database of genus-<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif"…

### Analytic monoids and factorization problems

- MathematicsSemigroup Forum
- 2016

The main goal of this paper is to initiate study of analytic monoids as a general framework for quantitative theory of factorization. So far the latter subject was developed either in concrete…

### Multiplicity one for $L$-functions and applications

- Mathematics
- 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.…

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