Research Repository

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Holomorphic automorphic forms and cohomology (2018)
Journal Article
Bruggeman, R., Choie, Y., & Diamantis, N. (in press). Holomorphic automorphic forms and cohomology. Memoirs of the American Mathematical Society, 253(1212), doi:10.1090/memo/1212. ISSN 0065-9266

We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least 2 this correspondence is given by the Eichler integral. We use Knopp’s generaliz... Read More

Period polynomials, derivatives of L-functions, and zerosof polynomials (2018)
Journal Article
Diamantis, N., & Rolen, L. (2018). Period polynomials, derivatives of L-functions, and zerosof polynomials. Research in the Mathematical Sciences, 5, doi:10.1007/s40687-018-0126-4

Period polynomials have long been fruitful tools for the study of values of L-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We discuss ways to... Read More

Regularized inner products and errors of modularity (2016)
Journal Article
Bringmann, K., Diamantis, N., & Ehlen, S. (2017). Regularized inner products and errors of modularity. International Mathematics Research Notices, 2017(24), doi:10.1093/imrn/rnw225. ISSN 1073-7928

We develop a regularization for Petersson inner products of arbitrary weakly holomorphic modular forms, generalizing several known regularizations. As one application, we extend work of Duke, Imamoglu, and Toth on regularized inner products of weakly... Read More

A correspondence of modular forms and applications to values of L-series (2015)
Journal Article
Diamantis, N., Neururer, M., & Strömberg, F. (in press). A correspondence of modular forms and applications to values of L-series. Research in Number Theory, 1(27), doi:10.1007/s40993-015-0029-z. ISSN 2363-9555

An interpretation of the Rogers–Zudilin approach to the Boyd conjectures is established. This is based on a correspondence of modular forms which is of independent interest. We use the reinterpretation for two applications to values of L-series and v... Read More

A converse theorem for double Dirichlet series and Shintani zeta functions (2014)
Journal Article
Diamantis, N., & Goldfeld, D. (2014). A converse theorem for double Dirichlet series and Shintani zeta functions. doi:10.2969/jmsj/06620449. ISSN 1881-1167

The main aim of this paper is to obtain a converse theorem for double Dirichlet series and use it to show that the Shintani zeta functions which arise in the theory of prehomogeneous vector spaces are actually linear combinations of Mellin transforms... Read More

Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions (2013)
Journal Article
Bringmann, K., Diamantis, N., & Raum, M. (2013). Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions. Advances in Mathematics, 233(1), doi:10.1016/j.aim.2012.09.025. ISSN 0001-8708

We introduce a new technique of completion for 1-cohomology which parallels the corresponding technique in the theory of mock modular forms. This technique is applied in the context of non-critical values of L-functions of GL(2) cusp forms. We prove... Read More