4 papers
Inequalities for inert primes and their applications
Zilong He
For any given non-square integer , we prove Euclid's type inequalities for the sequence of all primes satisfying the Kronecker symbol $ (D/q_{…
Sign changes of Fourier coefficients of cusp forms of half-integral weight over split and inert primes in quadratic number fields
Zilong He, Ben Kane
In this paper, we investigate sign changes of Fourier coefficients of half-integral weight cusp forms. In a fixed square class , we investigate the sign changes in t…
Regular ternary polygonal forms
Zilong He, Ben Kane
Inspired by Dickson's classification of regular ternary quadratic forms, we prove that there are no primitive regular -gonal forms when is sufficiently large. In order to do…
On the sum of reciprocal generalized Fibonacci numbers
Pingzhi Yuan, Zilong He, Junyi Zhuo
In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibona…