A still sharper region where p(x)

Saputer, YannickTrudgian, TimothyDemichel, Patrick2016-02-240025-5718http://hdl.handle.net/1885/98757We consider the least number x for which a change of sign of π(x) − li(x) occurs. First, we consider modifications of Lehman’s method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.A still sharper region where p(x) - li(x) is positive**201510.1090/S0025-5718-2015-02930-52016-02-24