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Kernels of L-functions and shifted convolutions (2020)
Journal Article
Diamantis, N. (2020). Kernels of L-functions and shifted convolutions. Proceedings of the American Mathematical Society, 148, 5059-5070. https://doi.org/10.1090/proc/15182

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... Read More about Kernels of L-functions and shifted convolutions.

Period functions associated to real-analytic modular forms (2020)
Journal Article
Diamantis, N., & Drewitt, J. (2020). Period functions associated to real-analytic modular forms. Research in the Mathematical Sciences, 7(3), https://doi.org/10.1007/s40687-020-00221-8

We define L-functions for the class of real-analytic modular forms recently introduced by F. Brown. We establish their main properties and construct the analogue of period polynomial in cases of special interest, including those of modular iterated i... Read More about Period functions associated to real-analytic modular forms.