On an Analogue of Titchmarsh’s Divisor Problem for Holomorphic Cusp Forms

the estimation of (1.1) for ξ = 1 is related to the location of the zeros of ζ, which is the classical approach to the prime number theorem, and for multiplicative ξ in general the problem can be related to the properties of a corresponding L-function in a similar way. (Chapter 5 of [13] contains a comprehensive discussion of this and related issues). A shift in the argument of ξ destroys the multiplicativity, however, and this approach to estimating (1.1) is not applicable. A classical example is Titchmarsh’s divisor problem, which considers the average value of the divisor function τ (n) at shifted primes, in other words, the estimation of