Journal of the Ramanujan Mathematical Society

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On Theta Series Attached to Maximal Lattices and Their Adjoints


Affiliations
1 Kunzenhof 4B, 79117 Freiburg, Germany
2 Lehrstuhl Dfur Mathematik, RWTH Aachen University, Germany
     

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The space Mk (N)* spanned by theta series of adjoints of maximal even lattices of exact level N, determinant N2 and dimension 2k has the Weierstrass property and hence allows us to define extremality for arbitrary squarefree level N. We find examples of such dual-extremal lattices. The space M(N)*=⊕kM2k (N)* is a free module of rank N over the ring of modular forms for the full modular group generated by homogeneous elements of weight ≤10.
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  • On Theta Series Attached to Maximal Lattices and Their Adjoints

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Authors

Siegfried Bocherer
Kunzenhof 4B, 79117 Freiburg, Germany
Gabriele Nebe
Lehrstuhl Dfur Mathematik, RWTH Aachen University, Germany

Abstract


The space Mk (N)* spanned by theta series of adjoints of maximal even lattices of exact level N, determinant N2 and dimension 2k has the Weierstrass property and hence allows us to define extremality for arbitrary squarefree level N. We find examples of such dual-extremal lattices. The space M(N)*=⊕kM2k (N)* is a free module of rank N over the ring of modular forms for the full modular group generated by homogeneous elements of weight ≤10.