Editing De Bruijn–Newman constant (section)

== Historical bounds ==
{| class="wikitable"

|+ Historical lower bounds

|-
!Year !! Lower bound on Λ !! Authors

|-
|1987 ||−50<ref>{{Cite journal|last1=Csordas|first1=G.|last2=Norfolk|first2=T. S.|last3=Varga|first3=R. S.|date=1987-09-01|title=A low bound for the de Bruijn-newman constant Λ|journal=Numerische Mathematik|language=en|volume=52|issue=5|pages=483–497|doi=10.1007/BF01400887|s2cid=124008641|issn=0945-3245}}</ref> || Csordas, G.; Norfolk, T. S.; Varga, R. S. 

|-
|1990 ||−5<ref>{{Cite journal|last=te Riele|first=H. J. J.|date=1990-12-01|title=A new lower bound for the de Bruijn-Newman constant|journal=Numerische Mathematik|language=en|volume=58|issue=1|pages=661–667|doi=10.1007/BF01385647|issn=0945-3245}}</ref> || te Riele, H. J. J.

|-
|1991
|−0.0991<ref>{{Cite journal|last1=Csordas|first1=G.|last2=Ruttan|first2=A.|last3=Varga|first3=R. S.|date=1991-06-01|title=The Laguerre inequalities with applications to a problem associated with the Riemann hypothesis|journal=Numerical Algorithms|language=en|volume=1|issue=2|pages=305–329|doi=10.1007/BF02142328|bibcode=1991NuAlg...1..305C|s2cid=22606966|issn=1572-9265}}</ref> || Csordas, G.; Ruttan, A.; Varga, R. S. 

|-
|1993 ||−5.895{{e|−9}}<ref>{{cite journal |last1=Csordas | first1=G. |last2=Odlyzko | first2=A.M. | author2-link=Andrew Odlyzko |last3=Smith | first3=W. | last4=Varga | first4=R.S. | author4-link=Richard S. Varga |title=A new Lehmer pair of zeros and a new lower bound for the De Bruijn–Newman constant Lambda |journal=[[Electronic Transactions on Numerical Analysis]] |volume=1 |pages=104–111 |year=1993 |url=http://www.dtc.umn.edu/~odlyzko/doc/arch/debruijn.constant.pdf |access-date=June 1, 2012 | zbl=0807.11059 }}</ref> || Csordas, G.; Odlyzko, A.M.; Smith, W.; Varga, R.S.

|-
|2000 ||−2.7{{e|−9}}<ref>{{cite journal |first1=A.M. |last1=Odlyzko | author-link=Andrew Odlyzko | title=An improved bound for the de Bruijn–Newman constant |journal=Numerical Algorithms |volume=25 |pages=293–303 |year=2000 |issue=1 | zbl=0967.11034 |bibcode=2000NuAlg..25..293O |doi=10.1023/A:1016677511798 |s2cid=5824729 }}</ref> || Odlyzko, A.M.

|-
|2011 ||−1.1{{e|−11}}<ref>{{cite journal
| last1 = Saouter | first1 = Yannick
| last2 = Gourdon | first2 = Xavier
| last3 = Demichel | first3 = Patrick
| doi = 10.1090/S0025-5718-2011-02472-5
| issue = 276
| journal = Mathematics of Computation
| mr = 2813360
| pages = 2281–2287
| title = An improved lower bound for the de Bruijn–Newman constant
| volume = 80
| year = 2011| doi-access = free
}}</ref> || Saouter, Yannick; Gourdon, Xavier; Demichel, Patrick

|-
|2018 || ≥0<ref name=":0" /> || Rodgers, Brad; Tao, Terence

|}

{| class="wikitable"

|+ Historical upper bounds

|-
!Year !! Upper bound on Λ !! Authors

|-
|1950 ||≤ 1/2<ref name="de Bruijn roots" /> || de Bruijn, N.G.
|-
|2008 ||< 1/2<ref name="Ki Kim Lee" /> || Ki, H.; Kim, Y-O.; Lee, J.

|-
|2019 ||≤ 0.22<ref name="Polymath15" /> || Polymath, D.H.J.

|-
|2020 ||≤ 0.2<ref name="Platt+Trudgian" /> || Platt, D.;  Trudgian, T.

|}