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Mellin Transform Formulas for Anderson Modules and Hints of Modularity

Oğuz Gezmiş, Nathan Green

math.NTarXiv:2608.03326

Abstract

In the present paper, we introduce formulas for the logarithm function of abelian, uniformizable Anderson modules. Combining our formulas with a motivic map introduced recently by the second author, we relate special values of dual Goss L-functions of Drinfeld modules to the rigid analytic trivialization of their corresponding t-comotives. We apply these formulas to relate certain L-values to special values of matrix valued modular forms, generalizing the vector valued Drinfeld modular forms of Pellarin and Pellarin and Perkins in the rank two setting.

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