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Can we remove the absolute value when doing Diophantine Approximation?

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#number-theory #analysis #diophantine-approximation
1.1k
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Show that $x^2 + y^2 = 3$ has no rational points

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#algebraic-geometry #rational-functions #diophantine-approximation #infinite-descent
174
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Any suggestions on how to compute $\limsup |\cos n|^{n^2}$?

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#number-theory #trigonometric-series #diophantine-approximation
649
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Exploiting a Diophantine approximation of $\pi^4$ into giving a series of rationals for $\pi^4$

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#sequences-and-series #analytic-number-theory #elliptic-curves #sums-of-squares #diophantine-approximation
84
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Motivation behind proof of Behrend's theorem on size of AP free subset

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#number-theory #analytic-number-theory #diophantine-approximation
67
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Why we get inequality form an equation?

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#real-analysis #inequality #proof-explanation #diophantine-equations #diophantine-approximation
141
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Finding the minimal value of a $4\times 4$ determinant

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#real-analysis #matrices #determinant #maxima-minima #diophantine-approximation
135
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A linear form can not be too small on integer points

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#real-analysis #irrational-numbers #rational-numbers #dual-spaces #diophantine-approximation
101
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Finding a minima for a linear form with integer coefficients

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#real-analysis #irrational-numbers #rational-numbers #diophantine-approximation #dual-spaces
139
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How many integer solutions are there to $x^4+y^4-x^2y^2=n$. Is there a generating function for this?

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#diophantine-equations #elliptic-curves #diophantine-approximation #theta-functions
124
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Approximating a real arbitrarily well by $Z$-linear combination of two reals having irrational ratio.

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#pigeonhole-principle #ergodic-theory #diophantine-approximation
163
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Siegel's lemma for arbitary number field.

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#number-theory #diophantine-equations #diophantine-approximation
146
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Does $lcm\{1,2,...,n\} = \prod_{p\leq n, p\in\mathbb{P}}p^{\lceil \frac{log(n)}{log(p)}\rceil}$?

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#number-theory #proof-verification #irrational-numbers #diophantine-approximation
161
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Irrationality measure of $\frac{\ln{3}}{\ln{2}}$.

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#number-theory #diophantine-approximation
130
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$0<|\sqrt a-\sqrt[3]b|<\epsilon$ for $a,b\in\Bbb Z_+$

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#number-theory #reference-request #diophantine-equations #approximation #diophantine-approximation

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