The Riemann Hypothesis remains one of mathematics’ most enduring and influential conjectures, proposing that all nontrivial zeros of the Riemann zeta function lie on the critical line where the real ...

Transactions of the American Mathematical Society, Vol. 363, No. 3 (MARCH 2011), pp. 1463-1485 (23 pages) We introduce certain integrals of a product of the Bernoulli polynomials and logarithms of ...

Dans sa preuve du théorème d'Apéry sur l'irrationalité de ζ(3), Beukers [B] a introduit des intégrales doubles et triples de fonctions rationnelles donnant de bonnes suites d'approximations ...

Multiple zeta functions extend the classical Riemann zeta function to several complex variables by involving multiple summations with distinct exponents. These functions not only encapsulate deep ...

Numbers like π, e and φ often turn up in unexpected places in science and mathematics. Pascal’s triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there’s the ...

The Riemann Hypothesis is widely regarded as the most important unsolved problem in mathematics. Put forward by Bernhard Riemann in 1859, it concerns the positions of the zeros of the Riemann zeta ...

Numbers like pi, e and phi often turn up in unexpected places in science and mathematics. Pascal's triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there's the ...

The Riemann hypothesis is the most important open question in number theory—if not all of mathematics. It has occupied experts for more than 160 years. And the problem appeared both in mathematician ...

Prime numbers, the indivisible atoms of arithmetic, seem to be strewn haphazardly along the number line, starting with 2, 3, 5, 7, 11, 13, 17 and continuing without pattern ad infinitum. But in 1859, ...

The Millennium Prize Problems, announced in 2000 by the Clay Mathematics Institute in the United States, are problems with a prize of $1 million (approximately 160 million yen). One of these problems ...