Abstract
Serre obtained the p-adic limit of the integral Fourier coefficients of modular forms on SL2(ℤ) for p = 2,3,5,7. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on Γ0(4N) for N = 1,2,4. The proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications to our main result, we obtain congruences on various modular objects, such as those for Borcherds exponents, for Fourier coefficients of quotients of Eisentein series and for Fourier coefficients of Siegel modular forms on the Maass Space.
| Original language | English |
|---|---|
| Pages (from-to) | 61-83 |
| Number of pages | 23 |
| Journal | Israel Journal of Mathematics |
| Volume | 175 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2010 Jan 1 |
| Externally published | Yes |
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- Mathematics(all)
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p-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight. / Choi, Dohoon; Choie, Y.
In: Israel Journal of Mathematics, Vol. 175, No. 1, 01.01.2010, p. 61-83.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - p-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight
AU - Choi, Dohoon
AU - Choie, Y.
PY - 2010/1/1
Y1 - 2010/1/1
N2 - Serre obtained the p-adic limit of the integral Fourier coefficients of modular forms on SL2(ℤ) for p = 2,3,5,7. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on Γ0(4N) for N = 1,2,4. The proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications to our main result, we obtain congruences on various modular objects, such as those for Borcherds exponents, for Fourier coefficients of quotients of Eisentein series and for Fourier coefficients of Siegel modular forms on the Maass Space.
AB - Serre obtained the p-adic limit of the integral Fourier coefficients of modular forms on SL2(ℤ) for p = 2,3,5,7. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on Γ0(4N) for N = 1,2,4. The proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications to our main result, we obtain congruences on various modular objects, such as those for Borcherds exponents, for Fourier coefficients of quotients of Eisentein series and for Fourier coefficients of Siegel modular forms on the Maass Space.
UR - http://www.scopus.com/inward/record.url?scp=77949934611&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77949934611&partnerID=8YFLogxK
U2 - 10.1007/s11856-010-0002-4
DO - 10.1007/s11856-010-0002-4
M3 - Article
AN - SCOPUS:77949934611
VL - 175
SP - 61
EP - 83
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
SN - 0021-2172
IS - 1
ER -