Modern Dynamics Seminar | Approximations by special values of the Riemann zeta function via cotangent integrals

Abstract：

In this talk, we will prove some approximation results by using a surprising cotangent integral identity which involves the ratio ζ(2k+1)/π^{2k+1}. This cotangent integral is more flexible in controlling coefficients of zeta values compared to the one developed by Alkan (Proc. Amer. Math. Soc. 143 (9) 2015, 3743–3752.). Let A be a sufficiently dense subset of {ζ(3),ζ(5),ζ(7)…}. We show that real numbers can be approximated by certain linear combinations of elements in A, where the coefficients are values of the derivatives of rational polynomials. This is a joint work with Dongsheng Wu.

Speaker

My main research interests are in the areas of number theory, analysis and special functions. Most of my research is centered around special values of L-functions and multiple zeta functions which play an important role at the interface of analysis, number theory, geometry and physics with applications ranging from periods of mixed Tate motives to evaluating Feynman integrals in quantum field theory. In my research, I employ methods from real & complex analysis and special functions. My future research directions include obtaining evaluations of Hoffman families of multiple zeta values and their L-values extensions. Moreover, I am also interested in connections with modular forms, special functions in p-adic setting, Mahler measure of multivariable polynomials and Chern-Simmons theory of knot invariants.