11:{"metadata":[["$","title","0",{"children":"Notes on Low discriminants and the generalized Newman conjecture"}],["$","meta","1",{"name":"description","content":"Generalizing work of Polya, de Bruijn and Newman, we allow the backward heat equation to deform the zeros of quadratic Dirichlet L-functions. There is a real constant \\Lambda_Kr (generalizing the de Bruijn-Newman constant \\Lambda) such that for time t>=\\Lambda_Kr all such L-functions have all their zeros on the critical line; for time t<\\Lambda_Kr there exist zeros off the line. Under GRH, \\Lambda_Kr<=0; we make the complementary conjecture 0<=\\Lambda_Kr. Following the work of Csordas et. al. on Lehmer pairs of Riemann zeros, we use low-lying zeros of quadratic Dirichlet L-functions to show that -1.13* 10^{-7}<\\Lambda_Kr. In the last section we develop a precise definition of a Low discriminant which is motivated by considerations of random matrix theory. The existence of infinitely many Low discriminants would imply 0<=\\Lambda_Kr."}],["$","meta","2",{"name":"author","content":"Jeffrey Stopple"}],["$","meta","3",{"name":"keywords","content":"Number Theory"}],["$","meta","4",{"name":"referrer","content":"origin"}],["$","meta","5",{"name":"robots","content":"index, follow"}],["$","link","6",{"rel":"canonical","href":"https://synthical.com/article/Notes-on-Low-discriminants-and-the-generalized-Newman-conjecture-8451889a-ffbd-11ed-9b54-72eb57fa10b3"}],["$","link","7",{"rel":"alternate","hrefLang":"de-DE","href":"https://synthical.com/article/Notes-on-Low-discriminants-and-the-generalized-Newman-conjecture-8451889a-ffbd-11ed-9b54-72eb57fa10b3/de"}],["$","link","8",{"rel":"alternate","hrefLang":"fr-FR","href":"https://synthical.com/article/Notes-on-Low-discriminants-and-the-generalized-Newman-conjecture-8451889a-ffbd-11ed-9b54-72eb57fa10b3/fr"}],["$","link","9",{"rel":"alternate","hrefLang":"es-ES","href":"https://synthical.com/article/Notes-on-Low-discriminants-and-the-generalized-Newman-conjecture-8451889a-ffbd-11ed-9b54-72eb57fa10b3/es"}],["$","link","10",{"rel":"alternate","hrefLang":"it-IT","href":"https://synthical.com/article/Notes-on-Low-discriminants-and-the-generalized-Newman-conjecture-8451889a-ffbd-11ed-9b54-72eb57fa10b3/it"}],["$","link","11",{"rel":"alternate","hrefLang":"ru-RU","href":"https://synthical.com/article/Notes-on-Low-discriminants-and-the-generalized-Newman-conjecture-8451889a-ffbd-11ed-9b54-72eb57fa10b3/ru"}],["$","meta","12",{"property":"og:title","content":"Notes on Low discriminants and the generalized Newman conjecture"}],["$","meta","13",{"property":"og:description","content":"Generalizing work of Polya, de Bruijn and Newman, we allow the backward heat equation to deform the zeros of quadratic Dirichlet L-functions. There is a real constant \\Lambda_Kr (generalizing the de Bruijn-Newman constant \\Lambda) such that for time t>=\\Lambda_Kr all such L-functions have all their zeros on the critical line; for time t<\\Lambda_Kr there exist zeros off the line. Under GRH, \\Lambda_Kr<=0; we make the complementary conjecture 0<=\\Lambda_Kr. Following the work of Csordas et. al. on Lehmer pairs of Riemann zeros, we use low-lying zeros of quadratic Dirichlet L-functions to show that -1.13* 10^{-7}<\\Lambda_Kr. In the last section we develop a precise definition of a Low discriminant which is motivated by considerations of random matrix theory. The existence of infinitely many Low discriminants would imply 0<=\\Lambda_Kr."}],["$","meta","14",{"property":"og:url","content":"https://synthical.com/article/Notes-on-Low-discriminants-and-the-generalized-Newman-conjecture-8451889a-ffbd-11ed-9b54-72eb57fa10b3"}],"$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20","$L21","$L22","$L23","$L24","$L25","$L26","$L27","$L28","$L29","$L2a","$L2b","$L2c","$L2d","$L2e","$L2f","$L30","$L31"],"error":null,"digest":"$undefined"}