On sums of a prime and four prime squares in short intervals

AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficiently large integer N≢1(mod3) can be written asN=p+p12+p22+p32+p42,with |p−N5|⩽N5U,|pj−N5|⩽U,j=1,2,3,4, where U=N41100+ε and p, pj are primes. This result improves a previous result with U=N41100+ε replaced by U=N511+ε

Sign changes of fourier coefficients of modular forms of half integral weight, 2

In this paper, we investigate the sign changes of Fourier coefficients of half-integral weight Hecke eigenforms and give two quantitative results on the number of sign changes

On a divisor problem related to the Epstein Zeta-Function, IV

International audienceIn this paper we study several divisor problems related to the Epstein zeta-function. We are able to improve previous results and establish some new results by applying some classical techniques

On a divisor problem related to the Epstein Zeta-Function, III

International audienceIn this paper we study the mean square of the error term ∆ * k (Q, x) in a divisor problem related to the Epstein zeta-function. An asymptotic formula has been obtained when k = 2