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Fourier coefficients of Jacobi forms over Cayley numbers.

Min King Eie (1995)

Revista Matemática Iberoamericana

In this paper we shall compute explicitly the Fourier coefficients of the Eisenstein seriesEk,m(z,w) = 1/2 ∑(c,d)=1 (cz + d)-k ∑t∈o exp {2πim((az + b/cz +d)N(t)) + σ(t,(w/cz +d) - (cN(w)/cz + d)}which is a Jacobi form of weight k and index m defined on H1 x CC, the product of the upper half-plane and Cayley numbers over the complex field C. The coefficient of e2πi(nz + σ(t,w)) with nm > N(t) has the form-2(k - 4)/Bk-4 ∏p SpHere Sp is an elementary factor which depends only on νp(m), νp(t),...

Fourier expansion along geodesics on Riemann surfaces

Anton Deitmar (2014)

Open Mathematics

For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.

From pseudodifferential analysis to modular form theory

André Unterberger (1999)

Journées équations aux dérivées partielles

Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.

Functoriality and the Inverse Galois problem II: groups of type B n and G 2

Chandrashekhar Khare, Michael Larsen, Gordan Savin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over ℚ ? Let ℓ be a prime and t a positive integer. We show that that the finite simple groups of Lie type B n ( ℓ k ) = 3 D S O 2 n + 1 ( 𝔽 ℓ k ) d e r if ℓ ≡ 3 , 5 ( mod 8 ) and G 2 ( ℓ k ) appear as Galois groups over ℚ , for some k divisible by t . In particular, for each of the two Lie types and fixed ℓ we construct infinitely many Galois groups but we do not have a precise control...

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