“Petersson trace formula”的意思、由来-开放百科全书

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Petersson trace formula

释义

References

In analytic number theory, the Petersson trace formula is a kind of orthogonality relation between coefficients of a holomorphic modular form. It is a specialization of the more general Kuznetsov trace formula.

In its simplest form the Petersson trace formula is as follows. Let be an orthonormal basis of , the space of cusp forms of weight on . Then for any positive integers we have

where is the Kronecker delta function, is the Kloosterman sum and is the Bessel function of the first kind.

References

* Henryk Iwaniec: Topics in Classical Automorphic Forms. Graduate Studies in Mathematics 17, American Mathematics Society, Providence, RI, 1991.

1 : Theorems in analytic number theory

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