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@article{Gro13,
  author  = {Gr{\"o}nwall, Thomas Hakon},
  title   = {Some asymptotic expressions in the theory of numbers},
  journal = {Transactions of the American Mathematical Society},
  volume  = {14},
  number  = {1},
  pages   = {113--122},
  year    = {1913},
  doi     = {10.2307/1988773}
}

@article{Ram97,
  author  = {Ramanujan, Srinivasa},
  title   = {Highly composite numbers},
  journal = {The Ramanujan Journal},
  volume  = {1},
  number  = {2},
  pages   = {119--153},
  year    = {1997},
  doi     = {10.1023/A:1009764017495},
  note    = {Annotated and with a foreword by Jean-Louis Nicolas and Guy Robin}
}

@article{AE44,
  author    = {Alaoglu, Leonidas and Erd\H{o}s, Paul},
  title     = {On highly composite and similar numbers},
  journal   = {Transactions of the American Mathematical Society},
  volume    = {56},
  number    = {3},
  pages     = {448--469},
  year      = {1944},
  doi       = {10.2307/1990319}
}

@article{EN75,
  author  = {Erd\H{o}s, Paul and Nicolas, Jean-Louis},
  title   = {R\'{e}partition des nombres superabondants},
  journal = {Bulletin de la Soci\'{e}t\'{e} Math\'{e}matique de France},
  volume  = {103},
  number  = {1},
  pages   = {65--90},
  year    = {1975},
  doi     = {10.24033/bsmf.1793}
}

@article{Rob84,
  author  = {Robin, Guy},
  title   = {Grandes valeurs de la fonction somme des diviseurs et hypoth\`{e}se de {R}iemann},
  journal = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es. Neuvi\`{e}me S\'{e}rie},
  volume  = {63},
  number  = {2},
  pages   = {187--213},
  year    = {1984}
}

@article{Lag02,
  author  = {Lagarias, Jeffrey C.},
  title   = {An elementary problem equivalent to the {R}iemann hypothesis},
  journal = {The American Mathematical Monthly},
  volume  = {109},
  number  = {6},
  pages   = {534--543},
  year    = {2002},
  doi     = {10.2307/2695443}
}

@article{Bri06,
  author  = {Briggs, Keith},
  title   = {Abundant numbers and the {R}iemann hypothesis},
  journal = {Experimental Mathematics},
  volume  = {15},
  number  = {2},
  pages   = {251--256},
  year    = {2006},
  doi     = {10.1080/10586458.2006.10128957}
}

@article{Cho+07,
  author    = {Choie, YoungJu and Lichiardopol, Nicolas and Moree, Pieter and Sol{\'{e}}, Patrick},
  title     = {On {R}obin's criterion for the {R}iemann hypothesis},
  journal   = {Journal de Th{\'{e}}orie des Nombres de Bordeaux},
  volume    = {19},
  number    = {2},
  pages     = {357--372},
  year      = {2007},
  doi       = {10.5802/jtnb.591}
}

@article{AF09,
  author  = {Akbary, Amir and Friggstad, Zachary},
  title   = {Superabundant numbers and the {R}iemann hypothesis},
  journal = {The American Mathematical Monthly},
  volume  = {116},
  number  = {3},
  pages   = {273--275},
  year    = {2009},
  doi     = {10.4169/193009709X470128}
}

@article{CNS12,
  author  = {Caveney, Geoffrey and Nicolas, Jean-Louis and Sondow, Jonathan},
  title   = {On {SA}, {CA}, and {GA} numbers},
  journal = {The Ramanujan Journal},
  volume  = {29},
  number  = {1--3},
  pages   = {359--384},
  year    = {2012},
  doi     = {10.1007/s11139-012-9371-0}
}

@article{NY14,
  author  = {Nazardonyavi, Sadegh and Yakubovich, Semyon},
  title   = {Extremely abundant numbers and the {R}iemann hypothesis},
  journal = {Journal of Integer Sequences},
  volume  = {17},
  number  = {2},
  year    = {2014}
}

@misc{VOJ20,
  author  = {Vojak, Robert},
  title   = {On numbers satisfying {R}obin's inequality, properties of the next counterexample and improved specific bounds},
  year    = {2020},
  eprint  = {2005.09307},
  archivePrefix = {arXiv},
  primaryClass  = {math.NT},
  note    = {Version 1 (submitted 19 May 2020)}
}

@article{Ban+09,
  author  = {Banks, William D. and Hart, Derrick and Moree, Pieter and Nevans, C. Wesley},
  title   = {The {N}icolas and {R}obin inequalities with sums of two squares},
  journal = {Monatshefte f\"{u}r Mathematik},
  volume  = {157},
  number  = {4},
  pages   = {303--322},
  year    = {2009},
  doi     = {10.1007/s00605-008-0022-x}
}

@article{SP12,
  author  = {Sol{\'{e}}, Patrick and Planat, Michel},
  title   = {The {R}obin inequality for 7-free integers},
  journal = {Integers},
  volume  = {12},
  number  = {2},
  pages   = {301--309},
  year    = {2012},
  doi     = {10.1515/integ.2011.103}
}

@article{BT15,
  author  = {Broughan, Kevin and Trudgian, Tim},
  title   = {Robin's inequality for 11-free integers},
  journal = {Integers},
  volume  = {15},
  year    = {2015}
}

@article{PM21,
  author  = {Platt, David J. and Morrill, Thomas},
  title   = {Robin's inequality for 20-free integers},
  journal = {Integers},
  volume  = {21},
  number  = {A28},
  year    = {2021}
}

@article{FRA22,
  title = {Robin's criterion on divisibility},
  author = {Vega, Frank},
  journal = {The Ramanujan Journal},
  publisher = {Springer},
  volume = {59},
  number = {3},
  pages = {745--755},
  year = {2022},
  doi = {10.1007/s11139-022-00574-4}
}

@article{DU21,
  title={On {R}obin's criterion for the {R}iemann {H}ypothesis},
  author={Aoudjit, Safia and Berkane, Djamel and Dusart, Pierre},
  journal={Notes on Number Theory and Discrete Mathematics},
  year={2021},
  volume={27},
  number={4},
  pages={15--24},
  doi = {10.7546/nntdm.2021.27.4.15-24}

}

@article{Her18,
  title={Robin's {I}nequality for {N}ew {F}amilies of {I}ntegers},
  author={Hertlein, Alexander},
  journal={Integers},
  volume={18},
  year={2018}
}

@inbook{CO15,
    author={Conrey, Brian},
    title={Riemann's hypothesis},
    series={Publications of the Scuola Normale Superiore (({COLLOQUIASNS},volume 5))},
    booktitle={Colloquium De Giorgi 2013 and 2014},
    year={2015},
    publisher={Scuola Normale Superiore},
    pages={109--117},
    doi={10.1007/978-88-7642-515-8_6}
}

@article{CO03,
  title={The {R}iemann {H}ypothesis},
  author={Conrey, Brian},
  journal={Notices of the AMS},
  volume={50},
  number={3},
  pages={341--353},
  year={2003}
}

@article{CO16,
  title={{A}n {E}ssay on the {R}iemann {H}ypothesis},
  author={Connes, Alain},
  doi={10.1007/978-3-319-32162-2_5},
  journal={Open Problems in Mathematics},
  pages={225--257},
  year={2016},
  publisher={Springer}
}

@article{RS62,
  author  = {Rosser, J. Barkley and Schoenfeld, Lowell},
  title   = {Approximate formulas for some functions of prime numbers},
  journal = {Illinois Journal of Mathematics},
  volume  = {6},
  number  = {1},
  pages   = {64--94},
  year    = {1962},
  doi     = {10.1215/ijm/1255631807}
}

@misc{VEG21,
  author       = {Vega, Frank},
  title        = {The {R}obin Inequality On Certain Numbers},
  year         = {2021},
  howpublished = {HAL preprint hal-03227797v2},
  url          = {https://hal.science/hal-03227797v2}
}

@book{Bor+08,
  author    = {Borwein, Peter B. and Choi, Stephen and Rooney, Brendan and Weirathmueller, Andrea},
  title     = {The {R}iemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike},
  series    = {CMS Books in Mathematics},
  volume    = {27},
  publisher = {Springer},
  address   = {New York},
  year      = {2008},
  doi       = {10.1007/978-0-387-72126-2}
}

@book{Edw01,
  author    = {Edwards, Harold M.},
  title     = {Riemann's Zeta Function},
  publisher = {Dover Publications},
  address   = {Mineola, NY},
  year      = {2001},
  isbn      = {0-486-41740-9}
}

@article{Axl18,
  author  = {Axler, Christian},
  title   = {New estimates for some functions defined over primes},
  journal = {Integers},
  volume  = {18},
  number  = {A52},
  year    = {2018}
}

@article{dVP99,
  author  = {de la Vall{\'e}e Poussin, Charles-Jean},
  title   = {Sur la fonction $\zeta(s)$ de {R}iemann et le nombre des nombres premiers inf{\'e}rieurs {\`a} une limite donn{\'e}e},
  journal = {M{\'e}moires Couronn{\'e}s et Autres M{\'e}moires Publi{\'e}s par l'Acad{\'e}mie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique},
  volume  = {59},
  year    = {1899}
}

@article{Mer74,
  author  = {Mertens, Franz},
  title   = {Ein {B}eitrag zur analytischen {Z}ahlentheorie},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume  = {78},
  pages   = {46--62},
  year    = {1874},
  doi     = {10.1515/crll.1874.78.46}
}