Timeline for what is the current best estimation for the upper bound of the exponential sum for an arbitrary irrational number $\alpha$

11 events

when toggle format	what		by	license	comment
Dec 25, 2023 at 7:15	history	edited	katago	CC BY-SA 4.0	edited body
Dec 22, 2023 at 21:31	history	edited	katago	CC BY-SA 4.0	deleted 23 characters in body
Dec 22, 2023 at 21:22	comment	added	katago		@Gerry Myerson Thank you for pointing it out, I apologize for not expressing it clearly. It refers to irrational numbers that satisfy the Diophantine condition. What I mean is that the last term of the continued fraction expansion of α can be well controlled by the previous terms. I think the Diophantine condition should be a slightly weaker control than the boundedness of the term of the continued fraction.
Dec 22, 2023 at 21:16	history	edited	katago	CC BY-SA 4.0	added 224 characters in body; edited title
Dec 22, 2023 at 21:13	history	edited	kodlu	CC BY-SA 4.0	edited title
Dec 22, 2023 at 19:29	comment	added	Gerry Myerson		What does it mean for a number to be "diophantine"?
Dec 21, 2023 at 18:36	comment	added	katago		If we drop the case of endpoints, this is equivalent to how bad the uniformity of the distribution of the values of a polynomial in a finite field of characteristic p becomes as p tends to infinity.
Dec 21, 2023 at 16:01	history	edited	katago	CC BY-SA 4.0	added 5 characters in body; edited title
Dec 21, 2023 at 15:35	history	edited	katago	CC BY-SA 4.0	added 18 characters in body; edited title
Dec 21, 2023 at 15:27	history	edited	katago	CC BY-SA 4.0	deleted 62 characters in body
Dec 21, 2023 at 15:03	history	asked	katago	CC BY-SA 4.0