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arXiv · 2308.06340

Tensor products of Drinfeld modules and convolutions of Goss $L$-series

Wei-Cheng Huang
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Abstract

Following the same framework of the special value results of convolutions of Goss and Pellarin $L$-series attached to Drinfeld modules that take values in Tate algebras by Papanikolas and the author, we establish special value results of convolutions of two Goss $L$-series attached to Drinfeld modules that take values in ${\mathbb{F}_q}(\!(\frac{1}{\theta})\!).$ Applying the class module formula of Fang to tensor products of two Drinfeld modules, we provide special value formulas for their $L$-functions. By way of the theory of Schur polynomials these identities take the form of specializations of convolutions of Rankin-Selberg type. Finally, we show an explicit computation of the regulators appearing in Fang's class module formula for tensor products as well as symmetric and alternating squares of Drinfeld modules.

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Wei-Cheng Huang. 2023-08-11. Tensor products of Drinfeld modules and convolutions of Goss $L$-series. https://arxiv.org/abs/2308.06340

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