We give a characterisation of the field into which quotients of values of L-functions associated to a cusp form belong. The construction involves shifted convolution series of divisor sums and to establish it we combine parts of F. Brown's technique to study multiple modular values with the properties of a double Eisentein series previously studied by the author and C. O'Sullivan.
Autocorrelation of ratios of L-functions
Subconvexity for $\rm{GL}(3)$ L-functions
Improved subconvexity bounds for GL(2)xGL(3) and GL(3) L-functions by weighted stationary phase
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