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Some Aspects of the Arithmetic Theory of Polynomials

  • Jun-ichi Igusa
Part of the Progress in Mathematics book series (PM, volume 67)

Abstract

This is an expository paper based on our memos of two lectures, one at the A.M.S. annual meeting at Cincinnati in January of 1982 with Professor Mostow presiding and another at the conference at Yale in honor of his 60th birthday. We have emphasized the universality or the uniformity of results and problems for all local fields; and consequently we have included certain material which is usually considered as analysis rather than arithmetic. On the other hand, as the title suggests, we have covered only certain parts of the arithmetic theory of polynomials. For instance the arithmetic theory of polynomials over a finite field is almost entirely left out. Also we have not given enough explanation to the recent results of Barlet [3] and Heath-Brown [11], which were mentioned at the time of the conference respectively by Professors Deligne and Tamagawa. Nevertheless it is our hope that this paper will give a fair and useful survey of certain parts of the arithmetic theory of polynomials appropriate for the Festschrift.

Keywords

Number Field Theta Series Meromorphic Continuation Gauge Form Arithmetic Theory 
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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Jun-ichi Igusa
    • 1
  1. 1.The Johns Hopkins UniversityBaltimoreUSA

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