期刊： JOURNAL OF NUMBER THEORY, 2021; 227 ()
The purpose of the present paper is to consider the extensibility of the Diophantine triple {a, b, c}, where a < b < c with b = 3a, and to prove......
期刊： JOURNAL OF NUMBER THEORY, 2021; 224 ()
We study the period integrals of Maass forms restricted to Hirzebruch-Zagier cycles of Hilbert surfaces. In particular, we shall prove an upper bound ......
期刊： JOURNAL OF NUMBER THEORY, 2021; 228 ()
In this paper, we study moments of the central values of quartic Dirichlet L-functions and establish quantitative non vanishing result for these L-val......
期刊： JOURNAL OF NUMBER THEORY, 2021; 225 ()
A folklore conjecture on the partition function asserts that the density of odd values of p(n) is 1/2. In general, for a positive integer t, let p(t)(......
期刊： JOURNAL OF NUMBER THEORY, 2021; 228 ()
For any positive integers k, m, n with m > 2 and k < n, let A(m, n, k) be the sum of all the multiple alternating zeta values of weight mn and d......
期刊： JOURNAL OF NUMBER THEORY, 2021; 224 ()
In the present paper, we prove the 2-part of Birch and Swinnerton-Dyer conjecture for an explicit infinite family of rank 0 quadratic twists of the mo......
期刊： JOURNAL OF NUMBER THEORY, 2021; 229 ()
For any prime p, let Rp be the set of all quadratic residues modulo p. In 2012, Sarkozy proved that if p is a sufficiently large prime, then Rp has no......
期刊： JOURNAL OF NUMBER THEORY, 2021; 227 ()
The Shortest Vector Problem and the computation of the tame kernel in algebraic K-theory are two different but very important problems, and up to now ......
期刊： JOURNAL OF NUMBER THEORY, 2021; 227 ()
Let g >= 3 be an integer. We show that the period of the generic genus g curve equals to 2g & minus; 2. We prove this by degenerating the gener......
期刊： JOURNAL OF NUMBER THEORY, 2021; 225 ()
In this paper, we proved the following theorem: Let beta and 251/252 < gamma < 1 be two real numbers. Then for almost all irrational alpha > ......
期刊： JOURNAL OF NUMBER THEORY, 2021; 229 ()
We study the parity of coefficients of classical mock theta functions. Suppose g is a formal power series with integer coefficients, and let c(g; n) b......
期刊： JOURNAL OF NUMBER THEORY, 2021; 229 ()
Let Fn be the Farey sequence of order n. For S subset of Fn we let Q(S) = {x/y : x, y E S, x < y and y not equal 0}. We show that if Q(S) C Fn, the......
期刊： JOURNAL OF NUMBER THEORY, 2021; 228 ()
We study the variance of the random variable that counts the number of lattice points in some shells generated by a special class of finite type domai......
期刊： JOURNAL OF NUMBER THEORY, 2021; 225 ()
In this paper, we prove that if f (x) = Sigma(n)(k=0) ((n)(k)) a(k)x(k) polynomial with real zeros only, then the sequence {a(k)}(k=0)(n) satisfies th......
期刊： JOURNAL OF NUMBER THEORY, 2021; 223 ()
Denote by P+(n) the largest prime factor of an integer n. In this paper, we show that the Elliott-Halberstam conjecture for friable integers (or smoot......
