@article{Sotelo-Pejerrey2023, 
author = {Alfredo Sotelo-Pejerrey},
title = {Traces of certain integral operators related to the Riemann hypothesis},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {24971-24983},
keywords = {singular trace, spectral trace, modified Fredholm determinant, Riemann hypothesis},
url = {https://www.sciopen.com/article/10.3934/math.20231274},
doi = {10.3934/math.20231274},
abstract = {We prove the existence of a nontrivial singular trace    τ defined on an ideal        J   closed with respect to the logarithmic submajorization such that    τ  (      A    ρ    (  α  )  )  =  0, where        A    ρ    (  α  )  :      L          2        (  0  ,  1  )  →      L          2        (  0  ,  1  ),        [          A      ρ        (    α    )    f    ]    (    θ    )    =          ∫              0                    1              ρ    (    α    θ          /        x    )    f    (    x    )    d    x  ,    0  <  α  ≤  1. We also show that    τ  (      A    ρ    (  α  )  )  =  0 for every    τ nontrivial singular trace on        J  . Finally, we give a recursion formula from which we can evaluate all the traces        Tr      (      A          ρ              r        (  α  )  ),    r  ∈      N  ,    r  ≥  2.}
}