学术动态

#Math101^†Session 2

Time：Sep. 15, 2021, 13:30--15:30

Location：434 Qi Xiang Building, Chang'an Campus

Speaker：Mr.Xu, Jiaru (Class of 2024)

Title：Rolle's theorem and zeros of generalized polynomials

Abstract：The fundamental theorem of algebrais undoubtedly one of the most famous existence theorems which shows that any non-zero polynomial has a number of zeros at most equal to its degree. When it comes topositivezeros, the basic result is known as Descartes' rule of signs. In this talk, we recollect the classical Rolle's theorem by which we derive Descartes' rule with its generalizations. Bounds of number of zeros of Dirichlet polynomials will be obtained in terms of sign changes in the sequence of coefficients and, in a finer degree, the sequence of their partial sums.Snacks and drinks will be provided.^††

† This is a series of seminars aimed at discussing mathematical analysis and advanced algebra of undergraduate level on a weekly basis. Contactshuangshen@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.