Premium
ON SIGN CHANGES FOR ALMOST PRIME COEFFICIENTS OF HALF‐INTEGRAL WEIGHT MODULAR FORMS
Author(s) -
Krishnamoorthy Srilakshmi,
Murty M. Ram
Publication year - 2016
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579316000048
Subject(s) - mathematics , ramanujan's sum , modular form , sign (mathematics) , prime (order theory) , conjecture , prime factor , pure mathematics , fourier series , prime number , siegel modular form , combinatorics , mathematical analysis
For a half‐integral weight modular form f = ∑ n = 1 ∞ a f ( n ) n ( k ‐ 1 ) / 2q nof weight k = ℓ + 1 / 2 onΓ 0 ( 4 )such thata f ( n )( n ∈ N ) are real, we prove for a fixed suitable natural number r thata f ( n )changes sign infinitely often as n varies over numbers having at most r prime factors, assuming the analog of the Ramanujan conjecture for Fourier coefficients of half‐integral weight forms.