A interpretation of the Rogers–Zudilin approach to the Boyd conjectures is established. This is based on a correspondence of modular forms which is of independent interest. We use the reinterpretation for two applications to values of L-series and values of their derivatives.
Daughton, A: A Hecke correspondence theorem for automorphic integrals with infinite log-polynomial sum period functions. Int. J. Number Theory. 10, 1857–1879 (2014).
Diamond, F, Shurman, J: A First Course in Modular Forms, Vol. 228. Springer-Verlag, New York (2005).
Goldfeld, D: Special values of derivatives of L-functions. Number theory (Halifax, NS, 1994), 159–173, CMS Conf. Proc., 15, Amer. Math. Soc., Providence, RI (1995).
Iwaniec, H: Topics in Classical Automorphic Forms. Graduate Studies in Mathematics, 17. American Mathematical Society, Providence, RI (1997).
Kohnen, W, Martin, Y: Products of two Eisenstein series and spaces of cusp forms of prime level. J. Ramanujan Math. Soc. 23, 337–356 (2008).
Rubinstein, M, Sarnak, P: Chebyshev’s bias. Experiment. Math. 3(3), 173–197 (1994).
Zudilin, W: Period(d)ness of L-values. Number theory and related fields, Springer Proc. Math. Stat, Vol. 43. Springer, New York (2013).
We are grateful to Kathrin Bringmann for drawing our attention to  and for many interesting discussions and to Don Zagier for many valuable comments on an early form of the note. We also thank Francois Brunault for reading carefully the submitted version of the paper and for offering very useful feedback. Finally we would like to thank the referee for very helpful comments that improved the exposition of the paper.
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Diamantis, N., Neururer, M. & Strömberg, F. A correspondence of modular forms and applications to values of L-series. Res. number theory 1, 27 (2015). https://doi.org/10.1007/s40993-015-0029-z
- Derivatives of L-functions
- Eisenstein series