Arithmetic properties of automorphic forms and Drinfeld modules

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My research area is number theory. It is a common phenomenon in mathematics that a number theoretical object can be associated with a complex function, in which important arithmetic data are encoded. For instance, the set of integers can be associated with the Riemann zeta function. In particular, the distribution of primes in integers can be associated with the non-trivial zeros of the Riemann zeta function. My work on number theory is to study these functions. One area I work in is the study of non-vanishing results on a certain family of such complex functions. Another area I work in is elliptic curves. The study of elliptic curves is important in modern number theory. The famous Fermat theorem was proved in 1995 by extended studies on this subject. A conjecture made by Birch and Swinnerton-Dyer predicts the deep connection between the arithmetic data of elliptic curves and the complex functions attached to elliptic curves. My results on these functions can help us better understand the conjecture of Birch and Swinnerton-Dyer.