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Subhajit Jana's user avatar
Subhajit Jana's user avatar
Subhajit Jana
  • Member for 11 years, 5 months
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Definition of Hecke operators
Great! So we can think $Gl_n(Z_p)\alpha Gl_n(Z_p)$ as all the Hecke operators? Is it true?
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Definition of Hecke operators
Much clear. Shouldn't that be $C_c^\infty( G(A_f) //K_f)$ (not sure)? Can we think $\Gamma\backslash G(R)$ as some copies of hyperbolic spaces?
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Definition of Hecke operators
Yes that is true. But are we using $\Gamma=K$ here?
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Mock Theta Functions
It would be great if Zwegers shares his motivation. Thanks for the reference.
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How to get an expression for this integral (Numerically/Analytically)
Can you please tell me how do $f,g$ look like, may be I can give something better.
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How to get an expression for this integral (Numerically/Analytically)
I think that if $f,g$ are polynomial above can be written as finite sum of some integrals. As we have, $$\sum_{n=0}^\infty P_n(t)x^n=(1-2tx+x^2)^{-1/2}.$$
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How to get an expression for this integral (Numerically/Analytically)
Oh I am sorry, that was a typo. I meant,$$\int_{\cos\alpha}^1\left(\sum_{n=0}^\infty f(n)P_n(t)\right)\left(\sum_{n=0}^\infty g(n)P_n(t)\right).$$
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How to get an expression for this integral (Numerically/Analytically)
If $f, g$ are polynomial, a closed form can possibly be given.
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A reformulation of the Riemann Hypothesis
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