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We investigate real values of the Riemann zeta function on the critical line. We show that if Gram's points do not intersect with the ordinates of the nontrivial zeros of the Riemann zeta function then the Riemann zeta function takes arbitrarily small real values on the critical line.

Small values of zeta-functions of quadratic fields.

John B. Friedlander (1978)

Mathematica Scandinavica

Small zeros of hermitian forms over a quaternion algebra

Wai Kiu Chan, Lenny Fukshansky (2010)

Acta Arithmetica

Small zeros of quadratic forms over algebraic function fields

Albrecht Pfister (1997)

Acta Arithmetica

Small-sum pairs in abelian groups

Reza Akhtar, Paul Larson (2010)

Journal de Théorie des Nombres de Bordeaux

Let $G$ be an abelian group and $A, B$ two subsets of equal size $k$ such that $A + B$ and $A + A$ both have size $2 k - 1$ . Answering a question of Bihani and Jin, we prove that if $A + B$ is aperiodic or if there exist elements $a \in A$ and $b \in B$ such that $a + b$ has a unique expression as an element of $A + B$ and $a + a$ has a unique expression as an element of $A + A$ , then $A$ is a translate of $B$ . We also give an explicit description of the various counterexamples which arise when neither condition holds.

Smooth solutions to the $a b c$ equation: the $x y z$ Conjecture

Jeffrey C. Lagarias, Kannan Soundararajan (2011)

Journal de Théorie des Nombres de Bordeaux

This paper studies integer solutions to the $a b c$ equation $A + B + C = 0$ in which none of $A, B, C$ have a large prime factor. We set $H (A, B, C) = max (| A |, | B |, | C |)$ , and consider primitive solutions ( $\gcd (A, B, C) = 1$ ) having no prime factor larger than ${(log H (A, B, C))}^{κ}$ , for a given finite $κ$ . We show that the $a b c$ Conjecture implies that for any fixed $κ < 1$ the equation has only finitely many primitive solutions. We also discuss a conditional result, showing that the Generalized Riemann hypothesis (GRH) implies that for any fixed $κ > 8$ the $a b c$ equation has infinitely many primitive solutions....

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Small Prime Solutions of some Additive Equations.

Small prime solutions of ternary linear equations

Small rational points on elliptic curves over number fields.

Small solutions of cubic equations with prime variables in arithmetic progressions

Small solutions of quadratic congruences and small fractional parts of quadratic forms

Small solutions to linear congruences and Hecke equidistribution

Small spanning sets of cusp forms.

Small value estimates for the multiplicative group

Small values of n2 ... (mod 1).

Small values of the Euler function and the Riemann hypothesis

Small values of the quadratic part of the Néron-Tate height on an abelian variety

Small values of the Riemann zeta function on the critical line

Small values of zeta-functions of quadratic fields.

Small zeros of hermitian forms over a quaternion algebra

Small zeros of quadratic forms over algebraic function fields

Small-sum pairs in abelian groups

Smooth solutions to the $a b c$ equation: the $x y z$ Conjecture

Smoothing Cusp Singularities of Small Length.

Sobre el cardinal de ciertos subconjuntos finitos del cuadrado unidad.

Sobre el índice de irregularidad de los números primos.

Currently displaying 261 – 280 of 1526