Timeline for Direct proof of special case of Hasse's theorem for elliptic curves

6 events

when toggle format	what		by	license	comment
Sep 21 at 16:10	history	edited	Alexey Ustinov	CC BY-SA 4.0	added 816 characters in body
Sep 20 at 19:41	comment	added	Alexey Ustinov		@MERTON $$\sum_{x=1}^{p-1}\left(\frac{x^4+n x}{p}\right)=\sum_{x=1}^{p-1}\left(\frac{x^{-4}+n x^{-1}}{p}\right)=\sum_{x=1}^{p-1}\left(\frac{1+n x^3}{p}\right)=\left(\frac{n}{p}\right) \sum_{x=0}^{p-1}\left(\frac{x^3+n^{-1}}{p}\right)$$
Sep 20 at 19:18	comment	added	Alexey Ustinov		@MERTON Jacobsthal and Schrutka studied such sums with $p(x)=x^3-ax$, $x^3-b$ and $x^4-a$.
Sep 19 at 18:37	comment	added	MERTON		This paper studies $\sum_i^{p-1} \Big(\frac{p(x)}{p}\Big)$ for polynomials of degree 1, 2, 4 but not 3. So I don't see how this can be related to elliptic curves
Jul 31 at 19:19	history	edited	Alexey Ustinov	CC BY-SA 4.0	added 178 characters in body
Jul 31 at 14:19	history	answered	Alexey Ustinov	CC BY-SA 4.0