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On special values of theta functions of genus two

Ehud De Shalit, Eyal Z. Goren (1997)

Annales de l'institut Fourier

We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.

On sums of Hecke series in short intervals

Aleksandar Ivić (2001)

Journal de théorie des nombres de Bordeaux

We have K - G k j K + G α j H j 3 ( 1 2 ) ϵ G K 1 + ϵ for K ϵ G K , where α j = ρ j ( 1 ) 2 ( cosh π k j ) - 1 , and ρ j ( 1 ) is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue λ j = k j 2 + 1 4 to which the Hecke series H j ( s ) is attached. This result yields the new bound H j ( 1 2 ϵ k j 1 3 + ϵ .

On sums of three squares

James W. Cogdell (2003)

Journal de théorie des nombres de Bordeaux

We address the question of when an integer in a totally real number field can be written as the sum of three squared integers from the field and more generally whether it can be represented by a positive definite integral ternary quadratic form over the field. In recent work with Piatetski-Shapiro and Sarnak we have shown that every sufficiently large totally positive square free integer is globally integrally represented if and only if it is so locally at all places, thus essentially resolving...

On the 4-norm of an automorphic form

Valentin Blomer (2013)

Journal of the European Mathematical Society

We prove the optimal upper bound f f 4 4 q ϵ where f runs over an orthonormal basis of Maass cusp forms of prime level q and bounded spectral parameter.

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