1933/01/01 by L. J. Mordell · 1 voice
Mathematics · #Iterative Methods for Nonlinear Equations #Advanced Mathematical Identities #Mathematics and Applications
paper · pdf · doi:10.1007/bf02547795
openalex publication_date 1933/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/04/06
in a memoir recently published dealing with the manuscripts left by Rienmnn has pointed out tllat Riemann deal~ with some integrals of the type [==j e~ t+ ddt in his researches on the zetafuuction. Not only can the usual functional equation be thus found, but also au asymptotic formula is obtained for the zetafunction of which the first term gives the well known approximate functional equation due to Hardy and Littlewood. -~ Kronecker's evaluation 3 of the Gauss's sums by special integrals of this kind is classic. Not so well known is his evaluation 8 of the integral oo C ~t'~In i Siegel 45--48. Hardy and Littlcwood (3), ~4/, ~ ~ ' ~5z.r 8 KroneCker (I), (2).