On a method of obtaining lower estimates for the number of sign-chances of certain arithmetical error-terms (Q1820811)

The authors first explain the method of the first author [Acta Arith. 44, 365-377 (1984; Zbl 0555.10023), and ibid. 45, 65-74 (1985; Zbl 0555.10024)] which was used successfully in obtaining lower bounds for sign changes of error terms in various forms of the prime number theorem. This method is then used to obtain a refinement of a result of J. Steinig on the number of sign changes of the error term in Dedekind's formula for the number of integral ideals with norm \(\leq x\) in number fields. In the course of the proof the authors evaluate some complicated sums involving generalized Bessel functions.