The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Remarks on Gaussian Sums and Tauberian Theorems


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

   Subscribe/Renew Journal


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.


Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 200

PDF Views: 0




  • Remarks on Gaussian Sums and Tauberian Theorems

Abstract Views: 200  |  PDF Views: 0

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.