@article{JTNB_2007__19_2_357_0, author = {Choie, YoungJu and Lichiardopol, Nicolas and Moree, Pieter and Sol\'e, Patrick}, title = {On Robin's criterion for the Riemann hypothesis}, journal = {Journal de th\'eorie des nombres de Bordeaux}, publisher = {Universit\'e Bordeaux 1}, volume = {19}, number = {2}, year = {2007}, pages = {357-372}, doi = {10.5802/jtnb.591}, mrnumber = {2394891}, zbl = {1163.11059}, language = {en}, url = {http://www.numdam.org/item/JTNB_2007__19_2_357_0} }
Choie, YoungJu; Lichiardopol, Nicolas; Moree, Pieter; Solé, Patrick. On Robin’s criterion for the Riemann hypothesis. Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 2, pp. 357-372. doi : 10.5802/jtnb.591. http://www.numdam.org/item/JTNB_2007__19_2_357_0/
[1] T. M. Apostol, Introduction to analytic number theory. Undergraduate Texts in Mathematics. Springer-Verlag, New York-Heidelberg, 1976. | MR 434929 | Zbl 0335.10001
[2] K. Briggs, Abundant numbers and the Riemann hypothesis. Experiment. Math. 15 (2006), 251–256. | MR 2253548 | Zbl pre05136954
[3] J. H. Bruinier, Primzahlen, Teilersummen und die Riemannsche Vermutung. Math. Semesterber. 48 (2001), 79–92. | MR 1950214 | Zbl 0982.11052
[4] S. R. Finch, Mathematical constants. Encyclopedia of Mathematics and its Applications 94, Cambridge University Press, Cambridge, 2003. | MR 2003519 | Zbl 1054.00001
[5] J. C. Lagarias, An elementary problem equivalent to the Riemann hypothesis. Amer. Math. Monthly 109 (2002), 534–543. | MR 1908008 | Zbl 1098.11005
[6] J.-L. Nicolas, Petites valeurs de la fonction d’Euler. J. Number Theory 17 (1983), 375–388. | Zbl 0521.10039
[7] S. Ramanujan, Collected Papers. Chelsea, New York, 1962.
[8] S. Ramanujan, Highly composite numbers. Annotated and with a foreword by J.-L. Nicolas and G. Robin. Ramanujan J. 1 (1997), 119–153. | MR 1606180 | Zbl 0917.11043
[9] G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann. J. Math. Pures Appl. (9) 63 (1984), 187–213. | MR 774171 | Zbl 0516.10036
[10] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers. Illinois J. Math. 6 (1962), 64–94. | MR 137689 | Zbl 0122.05001
[11] G. Tenenbaum, Introduction to analytic and probabilistic number theory. Cambridge Studies in Advanced Mathematics 46, Cambridge University Press, Cambridge, 1995. | MR 1342300 | Zbl 0831.11001