科研之友
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摘要
Given a finite set {T} of symmetric, positive definite, half-integral n by n matrices over Z which are inequivalent under the action of GL(n, Z), we show that the corresponding set of Poincare series {P-k(n) (T)} attached to them are linearly independent for weights k in infinitely many arithmetic progressions. We also give a quite explicit description of those arithmetic progressions for all even degrees, when the matrices T have no improper automorphisms and their level is an odd prime. Our main tools are theta series with simple harmonic polynomials as coefficients and techniques familiar from the theory of modular forms mod p.
- 出版日期2015-2
