Kernels of L-functions and shifted convolutions
  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. 
Nikolaos Diamantis
math.NT