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All Outputs (22)

On the standard L-function attached to quaternionic modular forms (2020)
Journal Article
Bouganis, A. (2021). On the standard L-function attached to quaternionic modular forms. Journal of Number Theory, 222, 293-345. https://doi.org/10.1016/j.jnt.2020.10.024

In this paper we study the analytic properties of the standard L-function attached to vector valued quaternionic modular forms using the Rankin-Selberg method. This involves the construction of vector valued theta series, which we obtain by applying... Read More about On the standard L-function attached to quaternionic modular forms.

On the Rankin-Selberg method for vector valued Siegel modular forms (2020)
Journal Article
Bouganis, A., & Mercuri, S. (2021). On the Rankin-Selberg method for vector valued Siegel modular forms. International Journal of Number Theory, 17(5), 1207-1242. https://doi.org/10.1142/s1793042121500330

In this work we use the Rankin-Selberg method to obtain results on the analytic properties of the standard L-function attached to vector valued Siegel modular forms. In particular we provide a detailed description of its possible poles and obtain a n... Read More about On the Rankin-Selberg method for vector valued Siegel modular forms.

Algebraicity of special L-values attached to Siegel-Jacobi modular forms (2020)
Journal Article
Bouganis, A., & Marzec, J. (2021). Algebraicity of special L-values attached to Siegel-Jacobi modular forms. manuscripta mathematica, 166(3-4), 359-402. https://doi.org/10.1007/s00229-020-01243-w

n this work we obtain algebraicity results on special L-values attached to Siegel–Jacobi modular forms. Our method relies on a generalization of the doubling method to the Jacobi group obtained in our previous work, and on introducing a notion of nea... Read More about Algebraicity of special L-values attached to Siegel-Jacobi modular forms.

On the analytic properties of the standard L-function attached to Siegel-Jacobi modular forms (2019)
Journal Article
Bouganis, A., & Marzec, J. (2019). On the analytic properties of the standard L-function attached to Siegel-Jacobi modular forms. Documenta Mathematica, 24, 2613-2684. https://doi.org/10.25537/dm.2019v24.2613-2684

In this work we study the analytic properties of the standard L-function attached to Siegel-Jacobi modular forms of higher index, generalizing previous results of Arakawa and Murase. Moreover, we obtain results on the analytic properties of Klingen-t... Read More about On the analytic properties of the standard L-function attached to Siegel-Jacobi modular forms.

On special L-values attached to metaplectic modular forms (2017)
Journal Article
Bouganis, A. (2018). On special L-values attached to metaplectic modular forms. Mathematische Zeitschrift, 3-4, 725-740. https://doi.org/10.1007/s00209-017-1909-9

In this paper we establish some algebraic properties of special L-values attached to Siegel modular forms of half-integral weight, often called metaplectic modular forms. These results are motivated by some “exercises” left by Shimura to the reader i... Read More about On special L-values attached to metaplectic modular forms.

On the algebraicity of special L-values of Hermitian modular forms (2015)
Journal Article
Bouganis, A. (2015). On the algebraicity of special L-values of Hermitian modular forms. Documenta Mathematica, 20, 1293-1329

In this work we prove some results on the algebraicity of special L-values attached to Hermitian modular forms. Our work is based on techniques developed by Goro Shimura in his book “Arithmeticity in the Theory of Automorphic Forms”, and our results... Read More about On the algebraicity of special L-values of Hermitian modular forms.

On Special L-Values Attached to Siegel Modular Forms (2014)
Book Chapter
Bouganis, A. (2014). On Special L-Values Attached to Siegel Modular Forms. In A. Bouganis, & O. Venjakob (Eds.), Iwasawa theory 2012 : state of the art and recent advances (135-176). Springer Verlag. https://doi.org/10.1007/978-3-642-55245-8_4

In his admirable book “Arithmeticity in the Theory of Automorphic Forms” Shimura establishes various algebraicity results concerning special values of Siegel modular forms. These results are all stated over an algebraic closure of Q . In this article... Read More about On Special L-Values Attached to Siegel Modular Forms.

Non-abelian p-adic L-functions and Eisenstein series of unitary groups -The CM method (2014)
Journal Article
Bouganis, A. (2014). Non-abelian p-adic L-functions and Eisenstein series of unitary groups -The CM method. Annales de l'Institut Fourier, 64(2), 793-891. https://doi.org/10.5802/aif.2866

In this work we prove various cases of the so-called “torsion congruences” between abelian p-adic L-functions that are related to automorphic representations of definite unitary groups. These congruences play a central role in the non-commutative Iwa... Read More about Non-abelian p-adic L-functions and Eisenstein series of unitary groups -The CM method.

The Möbius–Wall congruences for p-adic L-functions of CM elliptic curves (2013)
Journal Article
Bouganis, A. (2014). The Möbius–Wall congruences for p-adic L-functions of CM elliptic curves. Mathematical Proceedings of the Cambridge Philosophical Society, 156(01), 183-192. https://doi.org/10.1017/s0305004113000625

In this paper we prove, under a technical assumption, the so-called “Möbius–Wall” congruences between abelian p-adic L-functions of CM elliptic curves. These congruences are the analogue of those shown by Ritter and Weiss for the Tate motive, and off... Read More about The Möbius–Wall congruences for p-adic L-functions of CM elliptic curves.

Non-abelian congruences between special values of L-functions of elliptic curves; the CM case (2011)
Journal Article
Bouganis, A. (2011). Non-abelian congruences between special values of L-functions of elliptic curves; the CM case. International Journal of Number Theory, 07(07), 1883-1934. https://doi.org/10.1142/s179304211100468x

In this work we prove congruences between special values of L-functions of elliptic curves with CM that seem to play a central role in the analytic side of the non-commutative Iwasawa theory. These congruences are the analog for elliptic curves with... Read More about Non-abelian congruences between special values of L-functions of elliptic curves; the CM case.

Special values of L-functions and false Tate curve extensions (2010)
Journal Article
Bouganis, A. (2010). Special values of L-functions and false Tate curve extensions. Journal of the London Mathematical Society, 82(3), 596-620. https://doi.org/10.1112/jlms/jdq041

In this paper we show how the p-adic Rankin–Selberg product construction of Hida can be combined with freeness results of Hecke modules of Wiles to establish interesting congruences between particular special values of L-functions of elliptic curves.... Read More about Special values of L-functions and false Tate curve extensions.

On the non-commutative Main Conjecture for elliptic curves with Complex Multiplication (2010)
Journal Article
Bouganis, A., & Venjakob, O. (2010). On the non-commutative Main Conjecture for elliptic curves with Complex Multiplication. Asian Journal of Mathematics, 14(3), 385-416. https://doi.org/10.4310/ajm.2010.v14.n3.a6

In [7] a non-commutative Iwasawa Main Conjecture for elliptic curves over Q has been formulated. In this note we show that it holds for all CM-elliptic curves E defined over Q. This was claimed in (loc. cit.) without proof, which we want to provide n... Read More about On the non-commutative Main Conjecture for elliptic curves with Complex Multiplication.

Algebraicity of L-values for elliptic curves in a false Tate curve tower (2007)
Journal Article
Bouganis, A., & Dokchitser, V. (2007). Algebraicity of L-values for elliptic curves in a false Tate curve tower. Mathematical Proceedings of the Cambridge Philosophical Society, 142(2), 193-204. https://doi.org/10.1017/s030500410600987x

Let E be an elliptic curve over , and τ an Artin representation over that factors through the non-abelian extension , where p is an odd prime and n, m are positive integers. We show that L(E,τ,1), the special value at s=1 of the L-function of the twi... Read More about Algebraicity of L-values for elliptic curves in a false Tate curve tower.