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### Is there a Grothendieck-Riemann-Roch type of theorem generalizing Grothendieck's Lefschetz trace formula

Grothendieck deduced that the L-function of a (constructible) $\ell$-adic sheaf on a variety over $\mathbf{F}_p$ is rational from the generalized trace formula.
My first question is based on the ...

**16**

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733 views

### Computation of low weight Siegel modular forms

We have these huge tables of elliptic curves, which were generated by computing modular forms of weight $2$ and level $\Gamma_0(N)$ as N increased.
For abelian surfaces over $\mathbb{Q}$ we have very ...

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166 views

### On Langlands Pairing and transfer factors

In the paper "On the definition of transfer factors" Langlands and Shelstad define a certain number of factors $\Delta_{I}$, $\Delta_{II}$,$\Delta_{III,1}$,$\Delta_{III,2}$, which are roots of unity.
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530 views

### base change and Langlands' combinatorial exercise

Hi,
Is it correct that Langlands' combinatorial exercise (as he terms it in his paper
"Shimura varieties and the Selberg trace formula") is to establish base change identities between orbital ...

**2**

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32 views

### Fundamental lemma: why is the transfer factor a power of q

Let $k$ be a finite field of sufficiently large characteristic, $F = k((t))$ and $\mathfrak{o} = k[[t]]$. Let $G$ be a reductive algebraic group defined over $\mathfrak{o}$. Roughly stated, for sake ...

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71 views

### Analytic continuation of intertwining operator

I was trying to understand the paper "Form of GL(2) from analaytic point of view", by Gelbart and Jacquet.
On Page 226 in Remark (4.13) they mention that the kernel of the local intertwining operator ...

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257 views

### on the fundamental lemma

I consider the fundamental lemma for the spherical Hecke algebra.
Let $G$ a connected reductive quasisplit group on $F$, a local field of equal characteristic $p$.
and $H$ an endoscopic group.
Can ...

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89 views

### About Theorem $3.1.3$ in Kubota's book: Elementary theory of eisenstein series

My question is about the proof of Theorem $3.1.3$ given in kubota's book, which shows how the function $\varphi(s)$ appearing in the Fourier expansion of eisenstein series can be continued ...

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39 views

### A source for integral operators in the context of Arthur-Selberg trace formula

Could you suggest a textbook for integral operators
(in the context of Arthur-Selberg trace formula)?