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Bochner, S.
- Theorems on Analytic Continuation which Occur in the Study of Riemann's Functional Equation
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1 Princeton University, US
1 Princeton University, US
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The Journal of the Indian Mathematical Society, Vol 21, No 3-4 (1957), Pagination: 127-147Abstract
The present paper is ostensibly a supplement to our recent paper [1] on Riemann's functional equation with multiple Gamma factors, which topic will be referred to in the last section; but in actuality we are interested in reviewing two lemmas needed for the purpose.
- Algebraic and Linear Dependence of Automorphic Functions in several Variables
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1 Princeton University, Princeton, N. J, US
1 Princeton University, Princeton, N. J, US
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The Journal of the Indian Mathematical Society, Vol 16 (1952), Pagination: 1-6Abstract
Theobem 1. Let S - S2k be a (non-compact) complex coordinate space of 2k real dimensions, and let S° be a domain in it whose closure S° can be covered by a finite number of allowable co-ordinate systems.- Remarks on Gaussian Sums and Tauberian Theorems
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1 Princeton University, Princeton, N.J., US
1 Princeton University, Princeton, N.J., US
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The Journal of the Indian Mathematical Society, Vol 15 (1951), Pagination: 97-104Abstract
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.
- On Compact Complex Manifolds
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1 Princeton University, US
1 Princeton University, US
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The Journal of the Indian Mathematical Society, Vol 11 (1947), Pagination: 1-21Abstract
In the present paper we will generalize a classical theorem (Theorem I) from one to several complex variables and we are justifying this undertaking on two counts. Firstly, the mere question of finding a suitable wording for the desired generalization will emphasize the discrepancy between one and several variables, and secondly our proof for the k-dimensional statements will be new even for the classical case k=I.- Connection between Functional Equations and Modular Relations, and Functions of Exponential Type
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1 Princeton University, Princeton. N. J, US
1 Princeton University, Princeton. N. J, US
Source
The Journal of the Indian Mathematical Society, Vol 16 (1952), Pagination: 99-102Abstract
In a recent paper (Some properties of modular relations, Annals of Math. 53 (1951), 332-363) we have re-studied the connection between functional equations for zeta functions and modular relations for theta functions from a rather broad approach (broad in a certain direction, that is), and it was pertinent to our approach to introduce a certain class of functions termed residual.- Hartogs' Theorem in Complex Spaces with Singularities
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Authors
S. Bochner
1,
W. T. Martin
2
Affiliations
1 Princeton University, Princeton, New Jersey, US
2 Massachusetts Institute of Technology, Cambridge, Massachusetts, US
1 Princeton University, Princeton, New Jersey, US
2 Massachusetts Institute of Technology, Cambridge, Massachusetts, US
Source
The Journal of the Indian Mathematical Society, Vol 16 (1952), Pagination: 137-146Abstract
Hartogs [3] has proved the following theorem distinctive of analytic functions in several complex variables.
Theorem A. If a function is defined in a domain of E2k, and if it is analytic in each variable separately, then it is analytic in all variables.