Zero of Special Functions

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This award provides support for two undergraduate researchers working under the supervision of the principal investigator on problems arising from number theory. It is concerned with the roots of L-functions of number fields and of algebraic curves. The Riemann zeta function is the most famous example of such an L-function. Knowledge of the precise location of the roots would have far reaching implications. For example, information on the roots of the zeta function relates to the distribution of prime numbers, while the roots of the L-function of a curve are related to the number of points on the curve. The students will study certain concrete cases - orthogonal polynomials which arise as Mellin transforms. They have a particularly simple form, and the background needed to analyze these functions is not extension. Symbolic computation using software such as Maple will play an important role in this work.