# On the holomorphy of exterior-square L-functions

@article{Belt2012OnTH, title={On the holomorphy of exterior-square L-functions}, author={Dustin David Belt}, journal={arXiv: Number Theory}, year={2012} }

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 this by establishing the nonvanishing of the local zeta integrals defined by Jacquet and Shalika for any fixed $s_0$. The even case is treated in detail. The odd case is treated briefly, in which case, the $L$-function is shown to be entire.

## 13 Citations

### LOCAL NEWFORMS AND FORMAL EXTERIOR SQUARE L-FUNCTIONS

- Mathematics
- 2013

Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations π of GLn(F). In this paper, we…

### On the local and global exterior square $L$-functions of $GL_n$

- Mathematics
- 2012

We show that the local exterior square L-functions of GLn constructed via the theory of integral representations by Jacquet and Shalika coincide with those constructed by the Langlands–Shahidi method…

### On the local and global exterior square L-functions

- Mathematics
- 2012

We show that the local exterior square L-functions of GL_n constructed via the theory of integral representations by Jacquet and Shalika coincide with those constructed by the Langlands-Shahidi…

### On the analytic properties of intertwining operators I: global normalizing factors

- Mathematics
- 2016

We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives of global normalizing factors associated to intertwining operators for the…

### Endoscopic transfer for unitary groups and holomorphy of Asai L-functions

- Mathematics
- 2015

The analytic properties of the complete Asai L-functions attached to cuspidal automorphic representations of the general linear group over a quadratic extension of a number field are obtained. The…

### The functional equation of the Jacquet-Shalika integral representation of the local exterior-square $L$-function

- Mathematics
- 2014

We prove the functional equation of the non archimedean exterior-square L-function of irreducible representations of GL(n), when n is odd.

### 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.…

### A weak form of beyond endoscopic decomposition for the stable trace formula of odd orthogonal groups

- Mathematics
- 2016

We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study…

### Analytic properties of automorphic L-functions and Arthur classification

- Mathematics
- 2014

Langlands spectral theory describes the residual spectrum of a reductive group in terms of intertwining operators and analytic properties of automorphic L-functions. On the other hand, according to…

### Shalika periods and parabolic induction for GL(n) over a non‐archimedean local field

- Mathematics
- 2015

Let F be a non‐archimedean local field, and n1 and n2 two positive even integers. We prove that if π1 and π2 are two smooth representations of GL(n1,F) and GL(n2,F) respectively, both admitting a…

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