Abstract
Let K0(VarQ)[1/L] denote the Grothendieck ring of Q-varieties with the Lefschetz class inverted. We show that there exists a K3 surface X over Q such that the motivic zeta function ζX(t):=∑n[SymnX]tn regarded as an element in K0(VarQ)[1/L][[t]] is not a rational function in t, thus disproving a conjecture of Denef and Loeser.
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