在本論文中，我們關注兩類t模，包括德林費爾模和卡利茨模的張量冪。在第一部分，我們關注這些t模上代數點之間的線性關係。更準確地說，我們研究了在這些t模上有限多個代數點馬瑟定理[Mas88]的類比。我們估計出這些t模上代數點之間線性關係 生成元大小的上界。在第二部分，我們研究了正特徵中的多重zeta值。我們討論了一些線性獨立結果，並為某些多重zeta值所張出的向量空間建立了維度的下界。最後，我們研究了[CM21]中引入的v-進位多重zeta值。我們證明對於任何固定指標，v-進位多重zeta值對於除了有限多個素點v之外的所有素點都是v-進位整數。此外，我們證明了某些情況下古庄-山下猜想對於v-進位多重zeta值的類比。

In this dissertation, we focus on two families of t-modules including Drinfeld modules and tensor powers of the Carlitz module. In the first part, we focus on the linear relations among algebraic points on these $t$-modules. More precisely, we study an analogue of Masser's theorem [Mas88] for finitely many algebraic points on these t-modules and consequently we derive an upper bound for the generators of F_q[t]-linear relations among them. In the second part, we study multiple zeta values in positive characteristic. We discuss some linear independence results and we established a lower bound of the dimension for certain vector spaces spanned by these values. Finally, we investigate v-adic multiple zeta values introduced in [CM21]. We prove that for any fixed index v-adic multiple zeta values are v-adic integers for all but finitely many places. Furthermore, we prove an analogue of a conjecture of Furusho and Yamashita for v-adic multiple zeta values for v a finite place of degree one.

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