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Polymath15, third thread: computing and approximating H_t

This is the third “research” thread of the Polymath15 project to upper bound the de Bruijn-Newman constant , continuing this previous thread. Discussion of the project of a non-research nature can continue for now in… 978 more words

Math.CA

Polymath15, second thread: generalising the Riemann-Siegel approximate functional equation

This is the second “research” thread of the Polymath15 project to upper bound the de Bruijn-Newman constant , continuing this previous thread. Discussion of the project of a non-research nature can continue for now in… 636 more words

Math.NT

Polymath15, first thread: computing H_t, asymptotics, and dynamics of zeroes

This is the first official “research” thread of the Polymath15 project to upper bound the de Bruijn-Newman constant . Discussion of the project of a non-research nature can continue for now in… 1,689 more words

Math.NT

The De Bruijn-Newman constant is non-negative

Brad Rodgers and I have uploaded to the arXiv our paper “The De Bruijn-Newman constant is non-negative“. This paper affirms a conjecture of Newman regarding to the extent to which the Riemann hypothesis, if true, is only “barely so”. 2,354 more words

Math.NT

An addendum to "amplification, arbitrage, and the tensor power trick"

In one of the earliest posts on this blog, I talked about the ability to “arbitrage” a disparity of symmetry in an inequality, and in particular to “amplify” such an inequality into a stronger one. 1,981 more words

Math.CA

On the sign patterns of entrywise positivity preservers in fixed dimension

Apoorva Khare and I have just uploaded to the arXiv our paper “On the sign patterns of entrywise positivity preservers in fixed dimension“. This paper explores the relationship between positive definiteness of Hermitian matrices, and entrywise operations on these matrices. 1,165 more words

Math.CA