Timeline for The Guinand-Weil explicit formula without entire function theory
Current License: CC BY-SA 3.0
15 events
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| Jan 28, 2012 at 16:01 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| May 1, 2011 at 22:47 | comment | added | Brad Rodgers | What would be especially interesting is for these statements to be true (in some sense) for the zeros of certain Beurling Zeta functions, but that there's not as nice an explicit formula as what I've written above seems to be a real roadblock. Perhaps that's a sign this hope is fruitless, or perhaps it just means the zeros of the Beurling Zeta function are not the right object to study. In general I'm just looking for a more structurally deep understanding at any rate. | |
| May 1, 2011 at 22:42 | comment | added | Brad Rodgers | Well, there's not a deep plan at this point; I'd just like to understand the explicit formula slightly better. (I have more analytic facility with harmonic analysis than complex analysis, for instance.) One reason I am interested in these things is to study statistical properties of the Riemann Zeta function; one can generally convert such statements into arithmetical statements, and it is elucidating to see if these statements are still true for the Beurling primes (often times they are!). (cont.) | |
| Apr 26, 2011 at 12:40 | comment | added | Marc Palm | and here the equivalence of poisson summation formula and functional equation: mathoverflow.net/questions/62969/… | |
| Apr 25, 2011 at 20:34 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Apr 25, 2011 at 20:28 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Apr 25, 2011 at 11:27 | comment | added | Marc Palm | Perhaps this article of Meyer arxiv.org/abs/math/0412277 gives a better start, since it only deals with the Riemann Zeta function without introducing nuclear bornological vector spaces and such... The adeles allow in his other article to threat all Hecke L-functions simultaneously, which makes everything only more conceptual so far. I am not sure how you want to construct your adeles or local fields for generalized primes anyway, if they are not associated to norms of prime ideals in a number field. Are you willing to share some rough ideas about your plans here? | |
| Apr 24, 2011 at 20:56 | vote | accept | Brad Rodgers | ||
| Apr 24, 2011 at 20:44 | comment | added | Brad Rodgers | Thanks! The article by Meyer at the end is I think exactly what I'm looking for; basically I'm looking to translate the complex analysis to harmonic analysis in as 'canonical' a way as possible. It will take me a little while to digest it though... | |
| Apr 24, 2011 at 14:11 | comment | added | SGP | Very nice answer! thanks for the insightful explanations! | |
| Apr 24, 2011 at 13:56 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Apr 24, 2011 at 13:49 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Apr 24, 2011 at 13:06 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Apr 24, 2011 at 13:00 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Apr 24, 2011 at 12:47 | history | answered | Marc Palm | CC BY-SA 3.0 |