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Title:
Sums of certain arithmetic functions over Fq[T] and symplectic and orthogonal distributions
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Abstract:
In 2018 Keating, Rodgers, Roditty-Gershon and Rudnick established relationships of the mean-square of sums of the divisor function dk(f) over short intervals and over arithmetic progressions for the function field Fq[T] to certain integrals over the ensemble of unitary matrices when q→∞ . We study similar problems leading to integrals over the ensembles of symplectic and orthogonal matrices when q→∞ . This is joint work with Vivian Kuperberg.
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