Outputs (35)

Period-like polynomials for L-series associated with half-integral weight cusp forms (2024)
Journal Article
Branch, J., Diamantis, N., Raji, W., & Rolen, L. (2024). Period-like polynomials for L-series associated with half-integral weight cusp forms. Research in the Mathematical Sciences, 11(3), Article 44. https://doi.org/10.1007/s40687-024-00455-w

Given the L-series of a half-integral weight cusp form, we construct polynomials behaving similarly to the classical period polynomial of an integral weight cusp form. We also define a lift of half-integral weight cusp forms to integral weight cusp f... Read More about Period-like polynomials for L-series associated with half-integral weight cusp forms.

L-values of harmonic Maass forms (2024)
Journal Article
Diamantis, N., & Rolen, L. (2024). L-values of harmonic Maass forms. Transactions of the American Mathematical Society, 377, 3905-3926. https://doi.org/10.1090/tran/9045

Bruinier, Funke, and Imamoglu have proved a formula for what can philosophically be called the "central L-value" of the modular j-invariant. Previously, this had been heuristically suggested by Zagier. Here, we interpret this "L-value" as the value o... Read More about L-values of harmonic Maass forms.

Analogues of the Bol operator for half-integral weight weakly holomorphic modular forms (2023)
Journal Article
Diamantis, N., Lee, M., & Rolen, L. (2023). Analogues of the Bol operator for half-integral weight weakly holomorphic modular forms. Proceedings of the American Mathematical Society, 152, 37-51. https://doi.org/10.1090/proc/16435

We define an analogue of the Bol operator on spaces of weakly holomorphic modular forms of half-integral weight. We establish its main properties and relation with other objects.

L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts (2022)
Journal Article
Diamantis, N., Lee, M., Raji, W., & Rolen, L. (2023). L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts. International Mathematics Research Notices, 2023(18), 15729-15765. https://doi.org/10.1093/imrn/rnac310

We introduce an L-series associated with harmonic Maass forms and prove their functional equations. We establish converse theorems for these L-series and, as an application, we formulate and prove a summation formula for the holomorphic part of a har... Read More about L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts.

Derivatives of L-series of weakly holomorphic cusp forms (2022)
Journal Article
Diamantis, N., & Stromberg, F. (2022). Derivatives of L-series of weakly holomorphic cusp forms. Research in the Mathematical Sciences, 9(4), Article 64. https://doi.org/10.1007/s40687-022-00363-x

Based on the theory of L-series associated with weakly holomorphic modular forms in Diamantis et al. (L-series of harmonic Maass forms and a summation formula for harmonic lifts. arXiv:2107.12366), we derive explicit formulas for central values of de... Read More about Derivatives of L-series of weakly holomorphic cusp forms.

Modular iterated integrals associated with cusp forms (2021)
Journal Article
Diamantis, N. (2022). Modular iterated integrals associated with cusp forms. Forum Mathematicum, 34(1), 157-174. https://doi.org/10.1515/forum-2021-0224

We construct an explicit family of modular iterated integrals which involves cusp forms. This leads to a new method of producing modular invariant functions based on iterated integrals of modular forms. The construction will be based on an extension... Read More about Modular iterated integrals associated with cusp forms.

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), Article 21. 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.

Eichler cohomology and zeros of polynomials associated to derivatives of L-functions (2020)
Journal Article
Diamantis, N., & Rolen, L. (2021). Eichler cohomology and zeros of polynomials associated to derivatives of L-functions. Journal für die reine und angewandte Mathematik, 2021(770), 1-25. https://doi.org/10.1515/crelle-2020-0011

Additive twists and a conjecture by Mazur, Rubin and Stein (2019)
Journal Article
Diamantis, N., Hoffstein, J., Kıral, M., & Lee, M. (2020). Additive twists and a conjecture by Mazur, Rubin and Stein. Journal of Number Theory, 209, 1-36. https://doi.org/10.1016/j.jnt.2019.11.016

In this paper, a conjecture of Mazur, Rubin and Stein concerning certain averages of modular symbols is proved. To cover levels that are important for elliptic curves, namely those that are not square-free, we establish results about L-functions with... Read More about Additive twists and a conjecture by Mazur, Rubin and Stein.

Holomorphic automorphic forms and cohomology (2018)
Journal Article
Bruggeman, R., Choie, Y. J., & Diamantis, N. (2018). Holomorphic automorphic forms and cohomology. Memoirs of the American Mathematical Society, 253(1212), 1-182. https://doi.org/10.1090/memo/1212

© 2018 by the American Mathematical Society. All rights reserved. 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 corresp... Read More about Holomorphic automorphic forms and cohomology.