Stephen Lester, Nadav Yesha
Published 2014-04-06Version 1
We investigate the behavior of the divisor function in both short intervals and in arithmetic progressions. The latter problem was recently studied by \'E. Fouvry, S. Ganguly, E. Kowalski, and Ph. Michel. We prove a complementary result to their main theorem. We also show that in short intervals of certain lengths the divisor function has a Gaussian limiting distribution. The analogous problems for Hecke eigenvalues are also considered.
Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions
Square-full polynomials in short intervals and in arithmetic progressions
Squarefree polynomials and Mobius values in short intervals and arithmetic progressions
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