黎曼假设的二元幂级数方法
A 2-variable power series approach to the Riemann hypothesis
摘要：
本文考虑两个复变数的幂级数By（fb）（x）=S_（n=0）|.A_n^b x^n y^（n（n+1）/2）.，其中. (-1).^ n A_n^b是Riemann Xi函数的Maclaurin级数的非零系数。黎曼假设是断言B_1（f^b）的所有零点都是实数。本文证明了B_y（f^b）的每一个零点都是y中实系数幂级数的逆，且当|y| <0，2078.我们证明了一个常数T的存在性，类似于de Bruijn-Newman常数，满足：0= y =T当且仅当B_y（f^b）的所有零点都是实数。我们证明了1/4 = T = 1和T=1等价于黎曼假设。证明了黎曼假设也等价于B_y（f^b）的每个Jensen多项式的判别式在区间[1/4，1]上不为零|[.我们证明了黎曼假设蕴涵着B_y（f^b）的零点是单的，并且我们猜想倒数蕴涵是真的.
英文摘要：
We consider the power series in two complex variables By(fb)(x)=S_(n=0)|.A_n^b x^n y^(n(n+1)/2)., where .(-1).^n A_n^b are the non-zero coefficients of the Maclaurin series of the Riemann Xi function. The Riemann hypothesis is the assertion that all zeros of B_1 (f^b) are real. We prove that every zero of B_y (f^b) is the inverse of a power series in y with real coefficients, which converges for |y|<0,2078.... We show the existence of a constant T, similar to the de Bruijn-Newman constant, satisfying : 0= y =T if and only if all zeros of B_y (f^b) are real. We prove that 1/4 = T = 1 and that T=1 is equivalent to the Riemann hypothesis. We show that the Riemann hypothesis is also equivalent to what the discriminant of each Jensen polynomial of B_y (f^b) does not vanish on the interval [1/4,1|[. We prove the Riemann hypothesis implies that the zeros of B_y (f^b) are simple for 0<y<1, and we conjecture that the reciprocal implication is true.
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