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All Outputs (36)

The classification of higher-order cusp forms (2008)
Journal Article
Diamantis, N., & Sim, D. (2008). The classification of higher-order cusp forms. Journal für die reine und angewandte Mathematik, 2008(622), 121-153. https://doi.org/10.1515/CRELLE.2008.067

Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.

Iterated integrals and higher order automorphic forms (2006)
Journal Article
Diamantis, N., & Sreekantan, R. (2006). Iterated integrals and higher order automorphic forms. Commentarii Mathematici Helvetici, 81(2), 481–494. https://doi.org/10.4171/cmh/60

Higher order automorphic forms have recently been introduced to study important questions in number theory and mathematical physics. We investigate the connection between these functions and Chen's iterated integrals. Then using Chen's theory, we pro... Read More about Iterated integrals and higher order automorphic forms.

Kernels for products of L-functions
Journal Article
Diamantis, N., & O'Sullivan, C. Kernels for products of L-functions. Algebra and Number Theory, 7(8), https://doi.org/10.2140/ant.2013.7.1883

The Rankin-Cohen bracket of two Eisenstein series provides a kernel yielding products of the periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein series built with a double sum. We develop the properti... Read More about Kernels for products of L-functions.

Automorphic forms of higher order
Journal Article
Deitmar, A., & Diamantis, N. Automorphic forms of higher order. Journal of the London Mathematical Society, 80(1), https://doi.org/10.1112/jlms/jdp015

In this paper a theory of Hecke operators for higher-order modular forms is established. The definition of higher-order forms is extended beyond the realm of parabolic invariants. A canonical inner product is introduced. The role of representation th... Read More about Automorphic forms of higher order.