论文标题
假差异算术和Riemann假设的拒绝
Pseudodifferential arithmetic and a rejection of the Riemann hypothesis
论文作者
论文摘要
运算符的Weyl符号演算会导致构造，如果将符号占据符号，则具有以下属性的操作员对Riemann Zeta函数的零分解的一定分布：Riemann假设等于涉及该操作员的估计收集的有效性。假差异算术是伪差异操作者理论的新章节，使得在研究中的操作员有可能完全显式。从以下强烈的意义上讲，这以出乎意料的方式引起了猜想：Zeta函数的零积累在临界条的边界上，而非平凡零的实际部分没有孤立的点。
The Weyl symbolic calculus of operators leads to the construction, if one takes for symbol a certain distribution decomposing over the zeros of the Riemann zeta function, of an operator with the following property: the Riemann hypothesis is equivalent to the validity of a collection of estimates involving this operator. Pseudodifferential arithmetic, a novel chapter of pseudodifferential operator theory, makes it possible to make the operator under study fully explicit. This leads in an unexpected way to a disproof of the conjecture, in the following strong sense: zeros of the zeta function accumulate on the boundary of the critical strip, and the set of real parts of non-trivial zeros has no isolated point.
