All Outputs (35)

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.

The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology (2008)
Journal Article
Diamantis, N., & O’Sullivan, C. (2008). The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology. Transactions of the American Mathematical Society, 360(11), 5629-5666. https://doi.org/10.1090/s0002-9947-08-04755-7

Values of L-functions at integers outside the critical strip (2007)
Journal Article
Choie, Y., & Diamantis, N. (2007). Values of L-functions at integers outside the critical strip. Ramanujan Journal, 14, 339–350. https://doi.org/10.1007/s11139-007-9034-8

Rankin-Cohen brackets on higher order modular forms (2006)
Conference Proceeding
Choie, Y., & Diamantis, N. (2006). Rankin-Cohen brackets on higher order modular forms.

L-functions of second-order cusp forms (2006)
Journal Article
Diamantis, N., Knopp, M., Mason, G., & O’Sullivan, C. (2006). L-functions of second-order cusp forms. Ramanujan Journal, 12, 327–347. https://doi.org/10.1007/s11139-006-0147-2

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.

The geometry of certain cocycles associated to derivatives of L-functions (2005)
Journal Article
Diamantis, N. (2005). The geometry of certain cocycles associated to derivatives of L-functions. Forum Mathematicum, 17(5), 735–752. https://doi.org/10.1515/form.2005.17.5.735

Second order modular forms (2002)
Journal Article
Chinta, G., Diamantis, N., & O'Sullivan, C. (2002). Second order modular forms. Acta Arithmetica, 103, 209-223. https://doi.org/10.4064/aa103-3-2

Hecke operators and derivatives of L-functions (2001)
Journal Article
Diamantis, N. (2001). Hecke operators and derivatives of L-functions. Compositio Mathematica, 125(1), 39 - 54. https://doi.org/10.1023/A%3A1002648306247

Hecke theory of series formed with modular symbols and relations among convolution L -functions (2000)
Journal Article
Diamantis, N., & O'Sullivan, C. (2000). Hecke theory of series formed with modular symbols and relations among convolution L -functions. Mathematische Annalen, 318, 85-105. https://doi.org/10.1007/s002080000112

Special values of higher derivatives of L-functions (1999)
Journal Article
Diamantis, N. (1999). Special values of higher derivatives of L-functions. Forum Mathematicum, 11(2), 229- 252. https://doi.org/10.1515/form.1999.005

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.

A new multiple Dirichlet series induced by a higher-order form
Journal Article
Diamantis, N., & Deitmar, A. A new multiple Dirichlet series induced by a higher-order form. Acta Arithmetica, 142(4), https://doi.org/10.4064/aa142-4-1

Higher-order Maass forms
Journal Article
Bruggeman, R., & Diamantis, N. Higher-order Maass forms. Algebra and Number Theory, 6(7), https://doi.org/10.2140/ant.2012.6.1409

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.