The Journal of the Indian Mathematical Society

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Remarks on Gaussian Sums and Tauberian Theorems


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1 Princeton University, Princeton, N.J., United States
     

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Kronecker's derivation of the reciprocity formula for certain Gaussian sums from the modular relation

1/2 + Σ e-πn2/x = x1/2 {1/2+Σ e-πn2x}        (I)

is fundamentally an Abelian-Tauberian argument (see the (not very rigorous) discussion in [I , p. 1781]), and we will reproduce his argument in a general set-up, although we have no specific instances to offer other than those well known.


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  • Remarks on Gaussian Sums and Tauberian Theorems

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Authors

S. Bochner
Princeton University, Princeton, N.J., United States

Abstract


Kronecker's derivation of the reciprocity formula for certain Gaussian sums from the modular relation

1/2 + Σ e-πn2/x = x1/2 {1/2+Σ e-πn2x}        (I)

is fundamentally an Abelian-Tauberian argument (see the (not very rigorous) discussion in [I , p. 1781]), and we will reproduce his argument in a general set-up, although we have no specific instances to offer other than those well known.