In this paper we study the sum , where denotes number of divisors n and { p } is a sequence integers indexed by primes. Under certain assumptions show that aforementioned . As an application, consider case given Fourier coefficients modular form.

Abstract A common measure of a function's complexity is the count its stationary points. For complicated functions, this grows exponentially with volume and dimension their domain. In practice, averaged over class functions (the annealed average), but large numbers involved can produce averages biased by extremely rare samples. Typical counts are reliably found taking average logarithm quenched...

There has been some interest on how the average character degree affects structure of a finite group. We define, and denote by $ \mathrm{anz}(G) $, number zeros characters group G as in table divided irreducible $. show that if < 1 then is solvable also \frac{1}{2} supersolvable. characterise abelian groups showing \frac{1}{3} only abelian.