Results 91 to 100 of about 714,179 (209)

BOUNDED GAPS BETWEEN PRIMES IN NUMBER FIELDS AND FUNCTION FIELDS

, 2015
. The Hardy–Littlewood prime k-tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs of Zhang, Maynard, and Tao have nevertheless made significant progress ...
Lemke Oliver, Robert J., Paul Pollack, Thompson, Lola, Castillo, Abel, Robert J. Lemke Oliver, Hall, Chris, Abel Castillo, Pollack, Paul, Chris Hall, Lola Thompson   +9 more
core   +1 more source

Loops in AdS: from the spectral representation to position space. Part III

Journal of High Energy Physics
We study loop amplitudes in anti de-Sitter space via the spectral representation. We consider loops of spinning fields and in particular gauge fields, and derive various identities connecting different families of loop diagrams, at different number of ...
Dean Carmi
doaj   +1 more source

A generalization of arithmetic derivative to p-adic fields and number fields [PDF]

Notes on Number Theory and Discrete Mathematics
The arithmetic derivative is a function from the natural numbers to itself that sends all prime numbers to 1 and satisfies the Leibniz rule. The arithmetic partial derivative with respect to a prime p is the p-th component of the arithmetic derivative ...
Brad Emmons, Xiao Xiao
doaj   +1 more source

The size of wild Kloosterman sums in number fields and function fields

Journal d'Analyse Mathématique, 2023
We study p-adic hyper-Kloosterman sums, a generalization of the Kloosterman sum with a parameter k that recovers the classical Kloosterman sum when k=2, over general p-adic rings and even equal characteristic local rings. These can be evaluated by a simple stationary phase estimate when k is not divisible by p, giving an essentially sharp bound for ...
openaire   +2 more sources

Class Number in Constant Extensions of Function Fields [PDF]

Proceedings of the American Mathematical Society, 1972
Let F/K be a function field in one variable of genus g having the finite field K as exact field of constants. Suppose p is a rational prime not dividing the class number of F. In this paper an upper bound is derived for the degree of a constant extension E necessary to have p occur as a divisor of the class number of the field E.
openaire   +2 more sources

Pole-skipping for massive fields and the Stueckelberg formalism

Journal of High Energy Physics
Pole-skipping refers to the special phenomenon that the pole and the zero of a retarded two-point Green’s function coincide at certain points in momentum space.
Wen-Bin Pan, Ya-Wen Sun, Yuan-Tai Wang
doaj   +1 more source

Twists of Hooley's Δ-function over number fields

, 2019
We prove tight estimates for averages of the twisted Hooley Δ-function over arbitrary number ...
Sofos, Efthymios, Sofos, E.
core   +1 more source

Artin L-Functions for Abelian Extensions of Imaginary Quadratic Fields [PDF]

, 2005
Let F be an abelian extension of an imaginary quadratic field K with Galois group G. We form the Galois-equivariant L-function of the motive h(Spec F)(j) where the Tate twists j are negative integers.
Johnson, Jennifer Michelle
core   +1 more source

The relative class number one problem for function fields, I

, 2022
We reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field $\mathbb{F}_2$ and ...
Kedlaya, Kiran S.
core  

Class number in non Galois quartic and non abelian Galois octic function fields over finite fields

, 2006
International audienceWe consider a totally imaginary extension of a real extension of a rational function field over a finite field of odd characteristic.
Aubry, Yves
core   +1 more source