ON A CONJECTURE OF HASSE CONCERNING MULTIPLICATIVE RELATIONS OF GAUSSIAN SUMS.

Abstract

Hasse's conjecture over the multiplicative relations of Gaussian sums with e th power residue characters is confirmed when these sums are considered as ideals, and it is shown that the conjecture is false when these sums are considered merely as numbers. The Davenport-Hasse formula is transformed into a form analogous to the multiplication formula of the gamma function, and the Bernoulli polynomial of degree 1 defined over a cyclic group of finite order is the main tool to deal with the problem. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1966
Accession Number
AD0642915

Entities

People

  • Koichi Yamamoto

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Behavior And Behavior Mechanisms
  • Complex Variables
  • Functions (Mathematics)
  • Groups (Mathematics)
  • Human Behavior
  • Mathematics
  • Personality
  • Polynomials

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.