Non-Covering Congruence Systems over Fq[x]
Prior state unknown→proved
leading asymptotic determined up to a bounded q-dependent term
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number-theory / Function-field arithmetic
Non-Covering Congruence Systems over Fq[x]
Let $D_q(n)$ be the largest possible least degree of a polynomial omitted by a non-covering family of $n$ distinct-modulus congruence classes in $\mathbb{F}_q[x]$. What is its asymptotic size? The answer is $D_q(n) = \frac{n}{q-1} + O_q(1)$.
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Let $D_q(n)$ be the largest possible least degree of a polynomial omitted by a non-covering family of $n$ distinct-modulus congruence classes in $\mathbb{F}_q[x]$. What is its asymptotic size? The answer is $D_q(n) = \frac{n}{q-1} + O_q(1)$.
leading asymptotic determined up to a bounded q-dependent term
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