2,260 reputation
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bio website mat.ulaval.ca/hchapdelaine/…
location Quebec city
age 36
visits member for 3 years, 10 months
seen 11 hours ago

Oct
26
comment Characterizing the real analytic Eisenstein series
Dear GH, yes you are right. Sorry for not having understood the point of your comment. So as you wrote, one may write down the appropriate second order linear differential equation and then find its general solution. Another way to see it is to notice that at $s=1/2$ there is a cancellation of the poles of $\zeta(2s)$ and $\zeta(2-2s)$ so that the next leading term turns out to be precisely $\log(y)\sqrt{y}$. Thanks for being persistant!
Oct
26
revised Characterizing the real analytic Eisenstein series
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Oct
26
accepted Characterizing the real analytic Eisenstein series
Oct
23
comment Characterizing the real analytic Eisenstein series
Well, by subtracting $\xi(2s)$ to $E(z,s)$ combined with some growth estimate "seems to be close" to saying that $\xi(2s)y^s$ is part of the constant term of the Fourier series $E(z,s)$. For example, if $s=3/4$ it says that $E(z,s)$ behaves asymptotically exactly like $\xi(3/2)\cdot y^{3/4}$.
Oct
23
comment Characterizing the real analytic Eisenstein series
Dear Luis, this is a nice characterization. Of course specifying partly what the constant term of the Fourier series is, is not as much conceptual as what I was hoping at first, but may be one cannot do better than that.
Oct
23
comment Characterizing the real analytic Eisenstein series
Do you have any precise idea on how to fix it?
Oct
23
comment Characterizing the real analytic Eisenstein series
Thanks Matt, this is good observation! Probably, one should put some explicit restrictions on the constant $C(s)$ which appears implicitly in the big O notation of property (5).
Oct
23
revised Characterizing the real analytic Eisenstein series
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Oct
23
comment Characterizing the real analytic Eisenstein series
Dear Gunter Harder, I know what is wrong. In the formula appearing in the display if it is $\frac{\partial}{\partial s}E(z,s)$ and therefore this is why you pick up a $\log(y)$. So I think that what I wrote is correct.
Oct
23
revised Characterizing the real analytic Eisenstein series
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Oct
23
revised Characterizing the real analytic Eisenstein series
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Oct
23
comment Characterizing the real analytic Eisenstein series
Dear Kunnysan, thanks for pointing out the inconsistancy with the functional equation and the shift with the constant!
Oct
23
comment Characterizing the real analytic Eisenstein series
Dear GH, thanks for the comment you are perfectly. I'll add the Euler factor with the factor $1/2$ so that I at least get the right residues!
Oct
22
asked Characterizing the real analytic Eisenstein series
Oct
15
comment A simple proof that parallelizable oriented closed manifolds are oriented boundaries?
Yes indeed, the anecdote behind your first answer is quite inspiring!
Oct
15
accepted A simple proof that parallelizable oriented closed manifolds are oriented boundaries?
Oct
15
comment A simple proof that parallelizable oriented closed manifolds are oriented boundaries?
OK thanks! This is a very nice argument!
Oct
14
comment A simple proof that parallelizable oriented closed manifolds are oriented boundaries?
Dear Andras, what do you mean by "take all the posets"?
Oct
14
revised Intersection of a ring class field of a quadratic field K with the cyclotomic extension of K
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Oct
13
revised Intersection of a ring class field of a quadratic field K with the cyclotomic extension of K
edited title