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SPECIAL VALUES OF SHIFTED CONVOLUTION DIRICHLET SERIES

  • Michael H. Mertens (a1) and Ken Ono (a2)

Abstract

In a recent important paper, Hoffstein and Hulse [Multiple Dirichlet series and shifted convolutions, arXiv:1110.4868v2] generalized the notion of Rankin–Selberg convolution $L$ -functions by defining shifted convolution $L$ -functions. We investigate symmetrized versions of their functions, and we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and “mixed mock modular” forms.

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