Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Papanikolas, Matthew"'
We establish special value results of convolutions of Goss and Pellarin $L$-series attached to Drinfeld modules that take values in Tate algebras. Applying the class module formula of Demeslay to certain rigid analytic twists of one Drinfeld module b
Externí odkaz:
http://arxiv.org/abs/2206.14931
Autor:
Huang, Wei-Cheng, Papanikolas, Matthew
We analyze log-algebraic power series identities for formal groups of elliptic curves over $\mathbb{Q}$ which arise from modular parametrizations. We further investigate applications to special values of elliptic curve $L$-functions.
Comment: 12
Comment: 12
Externí odkaz:
http://arxiv.org/abs/2204.04719
In this paper we introduce the notion of Shimura's period symbols over function fields in positive characteristic and establish their fundamental properties. We further formulate and prove a function field analogue of Shimura's conjecture on the alge
Externí odkaz:
http://arxiv.org/abs/2203.09131
We develop tools for constructing rigid analytic trivializations for Drinfeld modules as infinite products of Frobenius twists of matrices, from which we recover the rigid analytic trivialization given by Pellarin in terms of Anderson generating func
Externí odkaz:
http://arxiv.org/abs/2104.02670
We investigate periods, quasi-periods, logarithms, and quasi-logarithms of Anderson $t$-modules, as well as their hyperderivatives. We develop a comprehensive account of how these values can be obtained through rigid analytic trivializations of abeli
Externí odkaz:
http://arxiv.org/abs/2103.05836
In this paper we prove a sparse equidistribution theorem for Gross points over the rational function field $\mathbb{F}_q(t)$. We apply this result to study the reduction map from CM Drinfeld modules to supersingular Drinfeld modules. Our proofs rely
Externí odkaz:
http://arxiv.org/abs/1905.07001
Autor:
Papanikolas, Matthew A.
We investigate interconnected aspects of hyperderivatives of polynomials over finite fields, q-th powers of polynomials, and specializations of Vandermonde matrices. We construct formulas for Carlitz multiplication coefficients using hyperderivatives
Externí odkaz:
http://arxiv.org/abs/1812.09739
The present article aims to provide a brief account of the theories of Drinfeld modules and Anderson's $t$-modules and $t$-motives. As such the article is not meant to be comprehensive, but we have endeavored to summarize aspects of the theory that a
Externí odkaz:
http://arxiv.org/abs/1806.03919
Autor:
Gezmiş, Oğuz, Papanikolas, Matthew A.
Publikováno v:
J. Algebra 525 (2019), 454-496
Introduced by Angl\`{e}s, Pellarin, and Tavares Ribeiro, Drinfeld modules over Tate algebras are closely connected to Anderson log-algebraicity identities, Pellarin $L$-series, and Taelman class modules. In the present paper we define the de Rham map
Externí odkaz:
http://arxiv.org/abs/1805.05386
Publikováno v:
J. Lond. Math. Soc. (2) 97 (2018), no. 2, 125-144
We formulate and prove a log-algebraicity theorem for arbitrary rank Drinfeld modules defined over the polynomial ring F_q[theta]. This generalizes results of Anderson for the rank one case. As an application we show that certain special values of Go
Externí odkaz:
http://arxiv.org/abs/1703.03368