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On the universality...
On the universality of the Epstein zeta function
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- Andersson, Johan, 1971- (författare)
- Mälardalens högskola,Utbildningsvetenskap och Matematik,Mathematics and Applied Mathematics
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- Anders, Södergren (författare)
- University of Copenhagen
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(creator_code:org_t)
- Engelska.
- Relaterad länk:
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http://arxiv.org/pdf...
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Abstract
Ämnesord
Stäng
- We study universality properties of the Epstein zeta function En(L,s) for lattices L of large dimension n and suitable regions of complex numbers s . Our main result is that, as n→∞ , En(L,s) is universal in the right half of the critical strip as L varies over all n -dimensional lattices L . The proof uses an approximation result for Dirichlet polynomials together with a recent result on the distribution of lengths of lattice vectors in a random lattice of large dimension and a strong uniform estimate for the error term in the generalized circle problem. Using the same basic approach we also prove that, as n→∞ , En(L1,s)−En(L2,s) is universal in the full half-plane to the right of the critical line as (L1,L2) varies over all pairs of n -dimensional lattices. Finally, we prove a more classical universality result for En(L,s) in the s -variable valid for almost all lattices L of dimension n . As part of the proof we obtain a strong bound of En(L,s) on the critical line that is subconvex for n≥5 and almost all n -dimensional lattices L.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Mathematics/Applied Mathematics
- matematik/tillämpad matematik
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