Mathematical Sciences: The Theta Correspondence and Central Derivatives of L-Functions

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The principal investigator will focus in on some problems involving theta functions, the Siegel-Weil formula, values and derivatives of L-functions and algebraic cycles on Shimura varieties. A generalization of the work of Waldspurger and of Gross and Zagier will be attempted, together with problems that concern the completion of the theory of the standard L-function for classical groups via the doubling method of Piatetski-Shapiro and Rallis. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.