250 research outputs found
On sign changes for almost prime coefficients of half-integral weight modular forms
For a half-integral weight modular form of weight on
such that ( ) are real, we prove for a fixed
suitable natural number that changes sign infinitely often as
varies over numbers having at most prime factors, assuming the analog of
the Ramanujan conjecture for half-integral weight forms.Comment: To appear in Mathematik
Special values of derivatives of -series and generalized Stieltjes constants
The connection between derivatives of for periodic arithmetical
functions at and generalized Stieltjes constants has been noted
earlier. In this paper, we utilize this link to throw light on the arithmetic
nature of and certain Stieltjes constants. In particular, if is
an odd prime greater than , then we deduce the transcendence of at least
of the generalized Stieltjes constants, , conditional on a conjecture of S. Gun, M. R. Murty and P. Rath.Comment: 11 page
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