Sign of Fourier coefficients of half-integral weight modular forms in arithmetic progressions
نویسندگان
چکیده
منابع مشابه
Sign Changes of Coefficients of Half Integral Weight Modular Forms
For a half integral weight modular form f we study the signs of the Fourier coefficients a(n). If f is a Hecke eigenform of level N with real Nebentypus character, and t is a fixed square-free positive integer with a(t) 6= 0, we show that for all but finitely many primes p the sequence (a(tp2m))m has infinitely many signs changes. Moreover, we prove similar (partly conditional) results for arbi...
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S. Chowla conjectured that every prime p has the property that there are infinitely many imaginary quadratic fields whose class number is not a multiple of p. Gauss’ genus theory guarantees the existence of infinitely many such fields when p = 2, and the work of Davenport and Heilbronn [D-H] suffices for the prime p = 3. In addition, the DavenportHeilbronn result demonstrates that a positive pr...
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In this paper we study the distribution of the coefficients a(n) of half integral weight modular forms modulo odd integers M . As a consequence we obtain improvements of indivisibility results for the central critical values of quadratic twists of L-functions associated with integral weight newforms established in [O-S]. Moreover, we find a simple criterion for proving cases of Newman’s conject...
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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.
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1. Introduction. Let k be an integer and N be a positive integer divisible by 4. If is a prime, denote by v a continuation of the usual-adic valuation on Q to a fixed algebraic closure. Let f be a modular form of weight k + 1/2 with respect to 0 (N) and Nebentypus character χ which has integral algebraic Fourier coefficients a(n), and put v (f) = inf n v (a(n)). Suppose that f is a common eigen...
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ژورنال
عنوان ژورنال: Research in Number Theory
سال: 2020
ISSN: 2522-0160,2363-9555
DOI: 10.1007/s40993-020-00225-x