学术动态

#Math101^†Session 6

Time：Oct. 20, 2021, 13:30--15:30

Location：434 Qi Xiang Building, Chang'an Campus

Speaker：Miss Sheng, Chen (Class of 2024)

Title：A one-to-one Riemann’s function

Abstract：The functions of Dirichlet and Riemann are first examples when we study continuity: the former isnowherecontinuous and the latter is continuousalmosteverywhere. Now in order to keep this feature but obtain a bijection from the real line to itself, the Dirichlet’s function may be modified by simply adding an identity; Riemann’s function is not the case, however.In this talk, we are interested in constructing a bijective Riemann-type function such that it is continuous at irrationals and discontinuous at rationals. The mainingredientis the Jacobsthal function g(n) which, for any natural number n,characterizes the maximal gapbetween consecutive integers coprime to n. Snacks and drinks will be provided.^††

† Seminars on analysis and algebra. Contact shuangshen@nwpu.edu.cn for any inquiry. For a history of this seminar, please visit https://teacher.nwpu.edu.cn/2017010194.

†† The refreshments are sponsored by a math competition mentors project, which is led by Prof. Ma, Rong. The support is gratefully acknowledged.