Timeline for The Guinand-Weil explicit formula without entire function theory
Current License: CC BY-SA 3.0
9 events
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| Oct 20, 2018 at 10:36 | comment | added | user23964 | with all the respect i have discovered that guinand weil formula can be extended to other arithmetical fucntion not only to the von mangoldt function vixra.org/pdf/1310.0048v4.pdf pages 6 to 10 | |
| Sep 22, 2015 at 13:44 | comment | added | Abdelmalek Abdesselam | another very nice introductory reference for the explicit formula is the article "The explicit formula in simple terms" by Jean-Francois Burnol available here arxiv.org/abs/math/9810169 | |
| Apr 25, 2011 at 7:18 | comment | added | Marc Palm | This is nothing deep with the eigenvalues, you just define $\sum\limits_{j} \lambda_j^{-s}$ for the set of eigenvalues of some operator. Of course, there should not be to many eigenvalues. There are also some work on explicit formulas by Lang-Jorgenson in some LNM. | |
| Apr 25, 2011 at 6:09 | comment | added | Brad Rodgers | There are functional equations of a rather limited sort, see section 3 of arxiv.org/PS_cache/math/pdf/0410/0410270v1.pdf. One has to define the notion of dual primes, and a lot of the elegance seems to be irretrievably lost. Could you elaborate on the point that we're choosing the Beurling primes to be the eigenvalues of some operator? This sounds interesting, but is mostly lost on me... Thanks again. | |
| Apr 24, 2011 at 20:56 | vote | accept | Brad Rodgers | ||
| Apr 24, 2011 at 15:05 | comment | added | Marc Palm | I refer to en.wikipedia.org/wiki/Beurling_zeta_function. It seems that a similar formula for the Beurling zeta function is not possible, i.e. you really need a functional equation to get an explicit description somewhere for real part small. It is very unlikely that there exists a functional equation for the spectral zeta function of some operator in general. Here, the Beurling zeta function is given by choosing the Beurling primes being the eigenvalues of some operator. | |
| Apr 24, 2011 at 12:47 | answer | added | Marc Palm | timeline score: 10 | |
| Apr 24, 2011 at 8:51 | history | edited | Brad Rodgers | CC BY-SA 3.0 |
added 30 characters in body
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| Apr 24, 2011 at 8:46 | history | asked | Brad Rodgers | CC BY-SA 3.0 |