## Research Abstracts Online

January 2010 - March 2011

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### University of Minnesota Twin Cities

College of Science and Engineering

School of Mathematics

# PI: Dennis A. Hejhal, Fellow

### Computational Aspects of Analytic Number Theory

These researchers are interested in linear combinations of L-functions and the distribution of their zeros. As part of this work, they are developing a new idea for calculating Euler products (L-functions) of higher orders utilizing a mixture of approximate functional equations and numerical analytic continuation via quadrature. They are using the supercomputers to conduct some pilot experiments to see if this method is feasible in practice. They are especially interested in L-functions associated with higher symmetric powers of automorphic representations, for which analytic continuation is only known conjecturally.

### Group Member

James Z. Wang, Information Technology, Pennsylvania State University, State College, Pennsylvania