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21/01/21 13:00 PM IST

New findings in number theory

In news

Interesting new findings on theoretical speculations in number theory may soon emerge from India

Highlights
  • Scientists are working on new cases of Stark conjectures, hypothetical information about the leading terms of L-functions in number theory.
  • These conjectures have direct applications to Hilbert’s 12th problem, one of the central problems in algebraic number theory. 
  • This theory has significance in cryptography, for instance, for generating elliptic curves for use in cryptosystems.
Number theory
  • It concerns the study of integer solutions to polynomial equations with integer coefficients. Solving such equations, in general, is challenging.
  • They are studied by attaching various invariants-- function, quantity, or property, which remains unchanged when a specific transformation is applied.
  • A very classical, fruitful, and much-studied invariant is the L-function (function on the complex plane, associated to one out of several categories of mathematical objects).
  • Some of the deepest problems in modern number theory are concerned with proving exact formulae for the values of L-functions at integer points in terms of purely arithmetic objects.
Source: PIB

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