Takeshi Saito is a Japanese mathematician known for his contributions to several areas of mathematics, particularly in algebraic geometry, topology, and singularity theory. His work often involves the study of algebraic varieties, deformation of singularities, and the relationship between algebraic geometry and mathematical physics. In particular, Saito is well-known for his development of the theory of mixed Hodge structures and for contributions to the theory of D-modules and their applications in singularity theory.

Tom M. Apostol (born March 20, 1923) is an American mathematician known for his contributions to various areas of mathematics, including number theory, algebra, and analysis. He is particularly famous for his textbooks, which are widely used in undergraduate and graduate courses. Apostol is perhaps best known for his two-volume work "Mathematical Analysis" and his books on number theory, including "Introduction to Analytic Number Theory.

Viggo Brun is a Norwegian mathematician known for his work in various areas of mathematics, particularly in number theory and analysis. He is notable for the Brun sieve, a technique he developed for finding prime numbers and studying their properties. The Brun sieve is a refinement of the traditional sieve methods and is particularly useful in analytic number theory.

W. R. (Red) Alford is a prominent figure in the field of education, particularly known for his contributions to educational administration and related academic areas. While specific details about his life and work may vary, he is often referenced in discussions about educational leadership and policy. If you are looking for information on a specific aspect of W. R.

William J. LeVeque (1912–1991) was an American mathematician renowned for his contributions to number theory and special functions. He is particularly well-known for his work in analytic number theory, including contributions to divisors of numbers, Riemann zeta functions, and L-functions. LeVeque authored several influential texts and papers, which have been utilized in various mathematical studies. His works often served as foundational resources for students and researchers in number theory.

Yitang Zhang is a Chinese-American mathematician known for his work in number theory, particularly in relation to the distribution of prime numbers. He gained significant attention in 2013 for proving a major result regarding the existence of bounded gaps between prime numbers. Specifically, he showed that there are infinitely many pairs of prime numbers that differ by a bounded amount, a breakthrough in the field of additive number theory.

Élisabeth Lutz is a French diplomat known for her work in various capacities, including her role within the French Ministry of Foreign Affairs. Her career has involved international relations and diplomatic efforts, although specific details about her accomplishments and positions may not be widely publicized.

Bauerian extension is a concept in the field of functional analysis and related areas of mathematics, particularly concerning the extension of linear operators or functionals from one space to another. It is named after the mathematician Friedrich Bauer. In a more specific context, consider the problem of extending bounded linear functionals defined on a subspace of a Banach space to the entire space.

The term "broken diagonal" can refer to different concepts depending on the context. Here are a few possible meanings: 1. **Mathematics or Geometry**: In geometry, a broken diagonal may refer to a piecewise linear path in a grid or a geometric figure that consists of segments forming a diagonal-like shape but is not a straight line. For instance, in a geometric grid, a broken diagonal could zigzag from one corner of a rectangle to the opposite corner.

An elementary number refers to a number that is part of basic arithmetic and number theory—specifically, it typically refers to the integers, rational numbers, or certain simple constructs in mathematics. The term can also refer to specific types of numbers, such as the natural numbers (1, 2, 3, ...), whole numbers (0, 1, 2, ...), negative integers, or even certain classes of rational numbers.

Ihara's lemma is a result in number theory, specifically in the study of zeta functions of curves over finite fields. The lemma relates the zeta function of a geometrically irreducible smooth projective curve over a finite field to the properties of its function field.

Legendre's conjecture is an unsolved problem in number theory that concerns the distribution of prime numbers. It posits that there is at least one prime number between every pair of consecutive perfect squares.

The HRS-100 is a human resource system that typically refers to personnel management software used by organizations to manage various HR tasks. However, the exact context and specifics can vary widely depending on the organization or industry. In some cases, it could also refer to a specific model or product related to human resources, such as a specific software or tool developed by a company.

Urban semiotics is an interdisciplinary field that studies the signs, symbols, and meanings within urban environments. It combines concepts from semiotics—the study of signs and meanings—with urban studies, focusing on how cities and urban spaces communicate cultural, social, and political messages. Key aspects of urban semiotics include: 1. **Signs and Symbols**: Urban semiotics examines physical elements like architecture, signage, public art, and urban design as forms of communication.

Shimura's reciprocity law is a profound result in the theory of numbers, particularly in the context of modular forms and the Langlands program. It generalizes classical reciprocity laws, such as those established by Gauss and later by Artin, to a broader setting involving Shimura varieties and abelian varieties. In essence, Shimura’s reciprocity law connects the arithmetic properties of abelian varieties defined over number fields to the values of certain automorphic forms.

The Siegel G-function is a complex function that arises in the theory of analytic number theory, particularly in the area of modular forms and automorphic forms. It is named after the German mathematician Carl Ludwig Siegel, who made significant contributions to number theory and related fields. In a broad sense, the Siegel G-function can be viewed as a generalization of the classical gamma function and is associated with several variables.

A **super-prime** is a special type of prime number that is itself prime and also has a prime index in the ordered sequence of all prime numbers.

A totally imaginary number field is a specific type of number field where every element of the field has its conjugates (in terms of field embeddings into the complex numbers) lying on the imaginary axis. More precisely, a number field is a finite extension of the field of rational numbers \(\mathbb{Q}\).

Lagrange's four-square theorem is a result in number theory that states that every natural number can be expressed as the sum of four integer squares.