{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:49:08Z","timestamp":1760402948871,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,4,26]],"date-time":"2020-04-26T00:00:00Z","timestamp":1587859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>This article presents the use of data processing to apprehend mathematical questions such as the Riemann Hypothesis (RH) by numerical calculation. Calculations are performed alongside graphs of the argument of the complex numbers     \u03b6  (  x + i y  )  = a + i b     and     \u03be  (  x + i y  )  = p + i q    , in the critical strip. On the one hand, the two-dimensional surface angle       tan   \u2212 1    (  b \/ a  )      of the Riemann Zeta function    \u03b6    is related to the semi-angle of the fractional part of      y  2 \u03c0   ln  (   y  2 \u03c0 e    )      and, on the other hand, the Ksi function    \u03be    of the Riemann functional equation is analyzed with respect to the coordinates      (  x , 1 \u2212 x ; y  )     . The computation of the power series expansion of the    \u03be    function with its symmetry analysis highlights the RH by the underlying ratio of Gamma functions inside the    \u03be    formula. The    \u03be    power series beside the angle of both surfaces of the    \u03b6    function enables to exhibit a B\u00e9zout identity     a u + b v \u2261 c     between the components      (  a , b  )      of the    \u03b6    function, which illustrates the RH. The geometric transformations in complex space of the Zeta and Ksi functions, illustrated graphically, as well as series expansions, calculated by computer, make it possible to elucidate this mathematical problem numerically. A final theoretical outlook gives deeper insights on the functional equation\u2019s mechanisms, by adopting a computer\u2013scientific perspective.<\/jats:p>","DOI":"10.3390\/info11050237","type":"journal-article","created":{"date-parts":[[2020,4,27]],"date-time":"2020-04-27T04:15:29Z","timestamp":1587960929000},"page":"237","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Calculations to Grasp a Mathematical Issue Such as the Riemann Hypothesis"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9561-7940","authenticated-orcid":false,"given":"Michel","family":"Riguidel","sequence":"first","affiliation":[{"name":"Department of Computer Science and Networks, T\u00e9l\u00e9com ParisTech, 75015 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,26]]},"reference":[{"key":"ref_1","unstructured":"Riemann, B. 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