강연자:  Bruce C. Berndt(University of Illinois at Urbana-Champaign) 명예교수

강연제목: Finite Trigonometric Sums

시간: 2025년 6월 12일 16시 30분

장소: 자연과학대학 5호관 201호

강연초록: Trigonometric sums arise in the famous, unsolved Dirichlet Divisor Problem. In his lost notebook, Ramanujan recorded an elegant identity connected with the Divisor Problem. This has led to sums of products of trig functions and several open problems connected with them. We evaluate analogues of Ramanujan sums, one of which leads to a theorem similar to the Franel–Landau criterion for the Riemann Hypothesis. Certain finite trigonometric sums are evaluated in closed form. Reciprocity and/or three sum relations are established for others. Much of this research was conducted with Sun Kim and Alexandru Zaharescu.