Results 11 to 20 of about 167,541,873 (127)

The Arithmetic of the Fourier Coefficients of Automorphic Forms [PDF]

, 2023
PhD thesis, 141 pages.
Davis, T
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Computation of Fourier coefficients of automorphic forms of type $$G_2$$ [PDF]

Research in Number Theory
In a recent work, we found formulas for the Fourier coefficients of automorphic forms of type $G_2$: holomorphic Siegel modular forms on $\mathrm{Sp}_6$ that are theta lifts from $G_2^c$, and cuspidal quaternionic modular forms on split $G_2$. We have implemented these formulas in the mathematical software SAGE.
Pollack, Aaron
core   +5 more sources

Higher-Dimensional Automorphic Lie Algebras. [PDF]

Found Comut Math, 2017
The paper presents the complete classification of Automorphic Lie Algebras based on sln(C)sln(C) , where the symmetry group G is finite and acts on sln(C)sln(C) by inner automorphisms, sln(C)sln(C) has no trivial summands, and where the poles are in ...
Knibbeler V, Lombardo S, Sanders JA.
europepmc   +3 more sources

Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups [PDF]

, 2022
In this paper we analyze Fourier coefficients of automorphic forms on adelic split simply-laced reductive groups $G(\mathbb{A})$. Let $\pi$ be a minimal or next-to-minimal automorphic representation of $G(\mathbb{A})$.
Gourevitch, Dmitry,, Kleinschmidt, Axel, Sahi, Siddhartha, Gustafsson, H., Kleinschmidt, A., Gustafsson, Henrik, Sahi, S., Persson, Daniel, Gourevitch, D., Persson, D., Sahi, Siddhartha,, Kleinschmidt, Axel,, Persson, Daniel,, Gourevitch, Dmitry, Gustafsson, Henrik,   +14 more
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Explicit calculations of automorphic forms for definite unitary groups [PDF]

, 2008
I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level G(^Z) and various small weights for an example of a rank 3 unitary group.
David Loeffler, Loeffler, David
core   +1 more source

Fourier expansion of light‐cone Eisenstein series

Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2175-2247, December 2023., 2023
Abstract In this work, we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n+1$n+1$‐space. As a consequence, we obtain results on location of all poles of these Eisenstein series as well as their supremum norms.
Dubi Kelmer, Shucheng Yu
wiley   +1 more source

Aspects of the screw function corresponding to the Riemann zeta‐function

Journal of the London Mathematical Society, Volume 108, Issue 4, Page 1448-1487, October 2023., 2023
Abstract We introduce a screw function corresponding to the Riemann zeta‐function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them can be considered an analog of so‐called Weil's positivity or Li's criterion.
Masatoshi Suzuki
wiley   +1 more source

A Burgess-like subconvex bound for twisted L-functions [PDF]

, 2007
Let g be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus, X a primitive character of conductor q, and s a point on the critical line Rs = 1/2.
Michel, Philippe, Blomer, Valentin, Mao, Z., Harcos, Gergely, Blomer, V., Michel, P., Harcos, G.   +6 more
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Fourier coefficients attached to small automorphic representations of SLn(A) [PDF]

, 2018
We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SLn(A) are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier
Kleinschmidt, Axel, Liu, Baiying, Liu, Baiying,, Baiying Liu, Gustafsson, H., Kleinschmidt, A., Gustafsson, Henrik, Gustafsson, Henrik H.P.A., Persson, Daniel, Daniel Persson, Gustafsson, Henrik P. A.,, Ahlen, Olof,, Ahlén, Olof, Persson, D., Henrik P.A. Gustafsson, Liu, B., Kleinschmidt, Axel,, Ahlen, O., Olof Ahlén, Persson, Daniel,, Axel Kleinschmidt, Gustafsson, Henrik,   +21 more
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Automorphic Lie algebras with dihedral symmetry [PDF]

, 2014
The concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems.
Sanders, Jan, Knibbeler, Vincent, Knibbeler, V., Lombardo, Sara, Lombardo, S., Knibbeler, V.; id_orcid, J A Sanders, Lombardo, S.; id_orcid, A Sanders, J., S Lombardo, V Knibbeler   +10 more
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