Titlebook: Automorphic Forms; Research in Number T Bernhard Heim,Mehiddin Al-Baali,Florian Rupp Conference proceedings 2014 Springer International Pub

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Going Amiss in Experimental ResearchThe paper describes the behaviour of octonionic theta constants under the restriction to the quaternionic half-space. As a result one can prove that the vector space, which is spanned by all restricted octonionic theta constants, coincides with the vector space spanned by quaternionic theta series of first respectively second kind.

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On the Special Values of Certain L-Series Related to Half-Integral Weight Modular Forms,Let . be a cuspidal Hecke eigenform of half-integral weight, and . be Cohen’s Eisenstein series of weight . For a Dirichlet character . we define a certain linear combination . of the Rankin–Selberg convolution products of . and . twisted by Dirichlet characters related with ..?We then prove a certain algebraicity result for . with . integers.

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The Restriction of Octonionic Theta Constants to the Quaternionic Half-Space,The paper describes the behaviour of octonionic theta constants under the restriction to the quaternionic half-space. As a result one can prove that the vector space, which is spanned by all restricted octonionic theta constants, coincides with the vector space spanned by quaternionic theta series of first respectively second kind.

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