Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Gezmiş, Oğuz"'
In the present paper, we determine the algebraic relations among the tractable coordinates of logarithms of Anderson $t$-modules constructed by taking the tensor product of Drinfeld modules of rank $r$ defined over the algebraic closure of the ration
Externí odkaz:
http://arxiv.org/abs/2407.18916
Autor:
Gezmiş, Oğuz, Green, Nathan
We introduce formulas for the logarithms of Drinfeld modules using a framework recently developed by the second author. We write the logarithm function as the evaluation under a motivic map of a product of rigid analytic trivializations of $t$-motive
Externí odkaz:
http://arxiv.org/abs/2405.02915
Autor:
Chen, Yen-Tsung, Gezmiş, Oğuz
In the present paper, we introduce the notion of nearly holomorphic Drinfeld modular forms and study an analogue of Maass-Shimura operators in this context. Furthermore, for a given nearly holomorphic Drinfeld modular form, we show that its special v
Externí odkaz:
http://arxiv.org/abs/2309.01761
Autor:
Chen, Yen-Tsung, Gezmiş, Oğuz
In this paper, we obtain an analogue of the Serre derivation acting on the product of spaces of Drinfeld modular forms which also generalizes the differential operator introduced by Gekeler in the rank two case. We further introduce a finitely genera
Externí odkaz:
http://arxiv.org/abs/2206.13997
Let $\mathbb{F}_q$ be the finite field with $q$ elements and consider the rational function field $K:=\mathbb{F}_q(\theta)$. For a Drinfeld module $\phi$ defined over $K$, we study the transcendence of special values of the Goss $L$-function attached
Externí odkaz:
http://arxiv.org/abs/2110.02569
Autor:
Chen, Yen-Tsung, Gezmiş, Oğuz
In the present paper, we introduce a special function on the Drinfeld period domain $\Omega^{r}$ for $r\geq 2$ which gives the false Eisenstein series of Gekeler when $r=2$. We also study its functional equation and relation with quasi-periodic funct
Externí odkaz:
http://arxiv.org/abs/2101.11819
Autor:
Gezmis, Oguz
Inspired by the classical setting, Goss defined $L$-series attached to Drinfeld modules. In this paper, for a fixed choice of a power $q$ of a prime number and a given Drinfeld module $\phi$ of rank 2 with a certain condition on its coefficients, we
Externí odkaz:
http://arxiv.org/abs/2005.13903
Autor:
Gezmiş, Oğuz
Publikováno v:
Documenta Mathematica 25, 2355--2411 (2020)
Pellarin introduced the deformation of multiple zeta values of Thakur as elements over Tate algebras. In this paper, we relate these values to a certain coordinate of a higher dimensional Drinfeld module over Tate algebras which we will introduce. Mo
Externí odkaz:
http://arxiv.org/abs/1910.02805
Autor:
Gezmiş, Oğuz
In the present paper, we analyze Taelman L-values corresponding to Drinfeld modules over Tate algebras of arbitrary rank. Using our results, we also introduce an L-series converging in Tate algebras which can be seen as a generalization of Pellarin L
Externí odkaz:
http://arxiv.org/abs/1807.01734
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