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A306936 Coefficients of q-expansion of Eisenstein series G_{9/2}(tau) multiplied by 240.

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%I A306936 #19 Feb 25 2024 12:41:34
%S A306936 1,2,0,0,242,480,0,0,2640,4322,0,0,11040,13920,0,0,30962,39360,0,0,
%T A306936 65760,73920,0,0,125280,156002,0,0,216960,226080,0,0,340560,406080,0,
%U A306936 0,522962,541920,0,0,756960,860160,0,0,1033440,1063200,0,0,1424160,1646402,0,0,1907040,1860000,0,0
%N A306936 Coefficients of q-expansion of Eisenstein series G_{9/2}(tau) multiplied by 240.
%H A306936 H. Cohen, <a href="https://doi.org/10.1007/BF01436180">Sums involving the values at negative integers of L-functions of quadratic characters</a>, Math. Ann. 217 (1975), no. 3, 271-285.
%H A306936 X. Wang and D. Pei, <a href="https://doi.org/10.1007/978-3-642-29302-3">Modular Forms with Integral and Half-Integral Weights</a>, Science Press Beijing, Springer Berlin Heidelberg, 2012. x+432 pp.
%H A306936 D. Zagier, <a href="https://people.mpim-bonn.mpg.de/zagier/files/tex/UtrechtLectures/UtBook.pdf">Modular Forms of One Variable</a>, Notes based on a course given in Utrecht, 1991. See page 50.
%o A306936 (Sage)
%o A306936 def a(n):
%o A306936     if n==0: return 1
%o A306936     if (n%4) not in [0, 1]: return 0
%o A306936     D = Integer(n).squarefree_part()
%o A306936     f = Integer(sqrt(n/D))
%o A306936     if (D%4) not in [0, 1]: D, f = 4*D, f//2
%o A306936     X = kronecker_character(D)
%o A306936     s = sum([moebius(d)*X(d)*d^3*sigma(f/d, 7) for d in f.divisors()])
%o A306936     return round((240*X.lfunction(100)(-3)*s).real()) # _Robin Visser_, Feb 24 2024
%Y A306936 Cf. A259825, A306934, A306935, A306937.
%K A306936 nonn
%O A306936 0,2
%A A306936 _N. J. A. Sloane_, Mar 16 2019
%E A306936 More terms from _Robin Visser_, Feb 24 2024