### Spectral construction of non-holomorphic Eisenstein-type series, their Kronecker limit formula and applications

Heilbronn Number Theory Seminar

29th May 2019, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

We discuss construction of a holomorphic form with a divisor D on a smooth, compact, projective Kähler variety X through the application of the Kronecker limit formula to a suitable integral (over D) of an Eisenstein-type series which is defined through a series of transformations of the heat kernel K_X, associated to the Laplacian that acts on the space of smooth functions on X. The special case of X being the n-dimensional complex projective space is further discussed and application of the Kronecker limit formula to computation of the Mähler measure of a linear form is presented. This work is joint with James Cogdell and Jay Jorgenson.

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