Goss zeta function

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In the field of mathematics, the Goss zeta function, named after David Goss, is an analogue of the Riemann zeta function for function fields. Sheats (1998) proved that it satisfies an analogue of the Riemann hypothesis. Kapranov (1995) proved results for a higher-dimensional generalization of the Goss zeta function.

David Goss American mathematician

David Mark Goss was a mathematician, a professor in the department of mathematics at Ohio State University, and the editor-in-chief of the Journal of Number Theory. He received his B.S. in mathematics in 1973 from University of Michigan and his Ph.D. in 1977 from Harvard University under the supervision of Barry Mazur; prior to Ohio State he held positions at Princeton University, Harvard, the University of California, Berkeley, and Brandeis University. He worked on function fields and introduced the Goss zeta function.

Riemann zeta function analytic function

The Riemann zeta function or Euler–Riemann zeta function, ζ(s), is a function of a complex variable s that analytically continues the sum of the Dirichlet series

In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex algebraic geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions.

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Conjecture proposition in mathematics that is unproven

In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof or disproof has yet been found. Conjectures such as the Riemann hypothesis or Fermat's Last Theorem have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.

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In mathematics, the Weil conjectures were some highly influential proposals by André Weil (1949), which led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory.

L-function

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Arithmetic geometry A branch of algebraic geometry focused on problems in number theory

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In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. The term "Shimura variety" applies to the higher-dimensional case, in the case of one-dimensional varieties one speaks of Shimura curves. Hilbert modular surfaces and Siegel modular varieties are among the best known classes of Shimura varieties.

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Ivan Fesenko is a mathematician working in number theory and its interaction with other areas of modern mathematics.

Christopher Deninger German mathematician

Christopher Deninger is a German mathematician at the University of Münster.

In mathematics, the arithmetic zeta function is a zeta function associated with a scheme of finite type over integers. The arithmetic zeta function generalizes the Riemann zeta function and Dedekind zeta function to higher dimensions. The arithmetic zeta function is one of the most-fundamental objects of number theory.

Kohji Matsumoto is a mathematician, Doctor of Mathematics, and professor of mathematics at Nagoya University in Nagoya, Japan. His specializations include number theory, zeta theory, and mathematical analysis. He is mostly recognized for the Matsumoto zeta function, a zeta function named after him. His academic papers have been published in several scientific journals. He co-edited Analytic Number Theory, a tome about prime numbers, divisor problems, Diophantine equations, and other topics related to analytic number theory, including Diophantine approximations, and the theory of zeta and L-functions. His other book, Algebraic And Analytic Aspects Of Zeta Functions And L-Functions, a compilation of lectures at the French-Japanese Winter School, was published in 2010.

Mikhail Kapranov, is a Russian mathematician, specializing in algebraic geometry representation theory, mathematical physics, and category theory.

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