Timeline for minimizing an integral over integer-coefficient polynomials $\displaystyle \inf_{f \in \mathbb{Z}[x]} \int_a^b f(x)^2 \, dx $ [duplicate]

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14 events

when toggle format	what		by	license	comment
Dec 4, 2014 at 21:27	history	closed	Felipe Voloch Ian Morris Peter Michor Neil Strickland Lucia		Duplicate of Hilbert's Theorem on $L_2$ norm of polynomials in $\mathbb{Z}[X]$ - Explicit construction and a converse?
Dec 4, 2014 at 21:12	vote	accept	john mangual
Dec 4, 2014 at 10:33	review	Close votes
Dec 4, 2014 at 21:27
Dec 4, 2014 at 6:12	answer	added	Noam D. Elkies		timeline score: 11
Dec 4, 2014 at 5:55	comment	added	Manfred Weis		to me it seems that the answer depends on the values of $a$ and $b$; if both are in the in the open interval $(-1,+1)$, then the infimum is $0$ and no minimum exists. I would therefore suggest to first clarify, how the answer is for $a=0,b\ge 1$ i.e. how it depends on $b$ in that case.
Dec 4, 2014 at 5:08	comment	added	Gerry Myerson		But the last line of the question still says "integer-valued".
Dec 4, 2014 at 3:40	history	edited	Michael Renardy	CC BY-SA 3.0	I assume you want f to be nonzero, otherwise there is an easy answer.
Dec 4, 2014 at 3:28	review	Suggested edits
Dec 4, 2014 at 3:30
Dec 4, 2014 at 3:10	comment	added	john mangual		@FelipeVoloch you are right. I have corrected the title
Dec 4, 2014 at 3:10	history	edited	john mangual	CC BY-SA 3.0	fixed an important typo
Dec 4, 2014 at 3:03	comment	added	Felipe Voloch		Integer valued polynomials is not the same as polynomials with integer coefficients. Which one do you want?
Dec 4, 2014 at 1:49	history	edited	Noam D. Elkies	CC BY-SA 3.0	$a_n \in \bf Z$, not $a$ which is the left endpoint
Dec 4, 2014 at 1:38	comment	added	BigM		You might find this LINK useful.
Dec 4, 2014 at 1:30	history	asked	john mangual	CC BY-SA 3.0