Giovanni De Gaetano
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 Jul10 comment Turning a Line Integral into a Contour one @DanielFischer Yes, this agrees with my computation. I think I could try to compute the additional pole (and relative residue) by brute force, but it's gonna be long and not elegant. While the observation of the authors of the paper on the possibility of turning it into a contour integral with only one pole is very tantalizing. Do you think it is possible to do that? On the other hand, according to the suggestions of Avitus I was trying to play a bit with different contours to exclude this additional pole. Thanks for your interest! Jul10 revised Turning a Line Integral into a Contour one added 1 characters in body Jul10 comment Turning a Line Integral into a Contour one Problems arise if I try some "classic" transformation. $z:=e^{i\theta}$ gives rise to a function holomorphic in $\mathbb{C}\setminus\{0\}$, but the integration path is not closed (it is the right semi-circle). For the transformation $z:=e^{2i\theta}$ the integration path is closed (the unit circle) but $i\sin(\theta)= \frac{1}{2}(\sqrt{z} -\frac{1}{\sqrt{z}})$ which is not holomorphic on the whole unit circle. I think those are just two expressions of the same pathology, i.e. the original integrand is not $\pi$-periodic. What do you think? Thanks again! Jul10 comment Turning a Line Integral into a Contour one @Avitus Thanks for your response! Actually we are supposed to consider both $B$ and $\lambda$ as parameters. As you say the imaginary part of the denominator is killed by $\theta=k\pi$, but the real part is always $\neq0$ for any $\theta$ (excluding at most 2 "annoying" choices of $\lambda$, but we are allowed to do it). In specific the integrand, as a function of $\theta$, is non singular. Jul10 asked Turning a Line Integral into a Contour one Jul1 comment Finding the integer solutions of $246x + 217y = 3$ Ooops, Clearly $7+1+2\neq 9$ then! I apologize for the mistake... ...in this case we simply observe that $3/3$ and $3/246$ implies that $3/y$ for any solution $y$. So all the solutions are of the form $(x_0,3y_0)$ where $(x_0,y_0)$ is a solution of $\frac{246}{3}x +217y =\frac{3}{3}$. The strategy of the comment above applies to this equation. PS @Tomas, thanks for pointing it out! Jul1 comment Finding the integer solutions of $246x + 217y = 3$ You can simplify the equation observing that all the coefficients are divisible by 3. Then apply the Euclidean algorithm en.wikipedia.org/wiki/Extended_Euclidean_algorithm to compute a solution, and finally use Bezout's identity en.wikipedia.org/wiki/Bézout's_identity to compute all of them. Jun25 comment How important are automorphic representations among admissible ones? Thanks! This is the kind of answer I was looking for! In specific I find extremely enlightening the observation about "factorization of automorphic forms" vs "factorization of automorphic representation", I completely oversaw it while studying! Jun25 accepted How important are automorphic representations among admissible ones? Jun20 asked How important are automorphic representations among admissible ones? Jun20 comment Definition of Automorphic Representation What is the definition of weakly contained in $L^2(G_F\backslash G_A)$? May13 comment Calculate an integral in a measurable space Could you post your proof that it is zero for any $\alpha>1$? I suspect that rearranging it one should be able to prove that the integral actually diverges for any $0<\alpha<1$. May7 awarded Caucus Apr23 revised Interpretation for the Functional Determinant deleted 2 characters in body Apr23 asked Interpretation for the Functional Determinant Apr22 comment Continuous dependence of zeros on a parameter Forcing a fixed number of solutions for any $\lambda$, keeping the interval $I$ open, should give you the result! Apr20 awarded Yearling Apr18 answered Continuous dependence of zeros on a parameter Apr18 comment Continuous dependence of zeros on a parameter Could you be a bit more explicit in what do you mean by "Assume its solutions are at least 1 and at most $n$ (not dependent on $\lambda$)"? Do you mean that for every $\lambda$ there are at most $n$ solutions? Or there is a finite and fixed number of solutions for every $\lambda$? Thank you! Apr16 comment Realization of Bessel functions You could be interested in what the DLMF (Digital Library of Mathematical Functions) has to say for the Bessel functions. Here is the link: dlmf.nist.gov/10 .