Papers 6,420

1 page of 642 pages (6,420 results)

Newest

Abstract We present a result that the modular equation of a Hauptmodul for a certain congruence subgroup Γ H ( N , t ) of genus zero satisfies Kronecker's congruence relation. This generalizes the author's previous result about Γ 1 ( m ) ⋂ Γ 0 ( m N ) . Furthermore we show that the similar result holds for a certain congruence subgroup Γ of genus zero with [ Γ : Γ H ( N , t ) ] = 2 . Finally we prove a conjecture of Lee and Park, asserting that the modular equation of the continued fraction of o...

Abstract null null We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference of the two preceding terms where the pluses and minuses follow a certain pattern. In 2012, McLellan proved that if the pluses and minuses follow a periodic pattern and null null null null null G null null null n null null null null null is th...

In this paper we associate to a linear differential equation with coefficients in the field of Laurent formal power series a new geometric object, a spectrum in the sense of Berkovich. We will compute this spectrum and show that it contains interesting informations about the equation.

Abstract For any integer K ≥ 1 , let s ( K ) be the smallest integer such that when the set of squares of the prime numbers is coloured in K colours, each sufficiently large integer can be written as a sum of no more than s ( K ) squares of primes, all of the same colour. We show that s ( K ) ≪ K exp ( ( 3 log 2 + o ( 1 ) ) log K log log K ) for K ≥ 2 . This upper bound for s ( K ) is close to optimal and improves on s ( K ) ≪ ϵ K 2 + ϵ , which is the best available upper bound for s (...

We propose a function-field analog of Pisot's dth root conjecture on linear recurrences, and prove it under some "non-triviality" assumption. Besides a recent result of Pasten-Wang on B{u}chi's dth power problem, our main tool, which is also developed in this paper, is a function-field analog of an GCD estimate in a recent work of Levin and Levin-Wang. As an easy corollary of such GCD estimate, we also obtain an asymptotic result.

Abstract Let l be an odd prime number and k = Q ( ζ + ζ − 1 ) where ζ is a primitive l-th root of unity. We provide a sufficient condition for the monogenity of a cyclic extension K s / k of degree l, where s is an integer of k and K s is a field defined by Rikuna's generic cyclic polynomial. As an application, we prove that there exist infinitely many monogenic extensions K s / k for l ≥ 5 . Keywords: monogenity, relative power integral basis, Rikuna's cyclic polynomial, Shintani's fundamental ...

Abstract Let d > 0 be a fundamental discriminant of a real quadratic field. Let h ( d ) be the class number and e d the fundamental unit of the real quadratic field Q ( d ) . In this paper, we prove that if there is an elliptic curve E over Q whose Hasse-Weil L-function L E / Q ( s ) has a zero of order g at s = 1 , then there is an effectively computable constant κ > 0 satisfying h ( d ) log e d > 1 κ ( log d ) g − 3 ∏ p | d , p ≠ d ( 1 − ⌊ 2 p ⌋ p + 1 ) .

Algebraicity of the near central non-critical values of symmetric fourth L-functions for Hilbert modular forms

Abstract null null Let Π be a cohomological irreducible cuspidal automorphic representation of null null null null null GL null null null 2 null null null ( null null null A null null null F null null null ) null null null with central character null null null null null ω null null null Π null null null null null over a totally real number field null null null F null null . In this paper, we prove the algebraicity of the near central non-critical value of the symmetric fourth L-function of Π twi...

Abstract null null Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of null null null S null ( null t null ) null null , null null null null null S null null null 1 null null null ( null t null ) null null , and null null null ζ null null ( null 1 null / null 2 null + null i null t null ) null null null null while comparing them with recently proven unconditional ones. As a corollary we obtain a conditional explicit bound on gaps between consecutive zeros of the Riema...

Abstract null null The purpose of the present paper is to give an effective version of the noncritical p-tame Belyĭ theorem. That is to say, we compute an explicit bound on the minimal degree of tamely ramified Belyĭ maps in positive characteristic which are unramified at a prescribed finite set of points.

12345678910