L-values for conductor 32

@article{Moerman2021LvaluesFC,
  title={L-values for conductor 32},
  author={Boaz Moerman},
  journal={Journal of Number Theory},
  year={2021}
}
  • Boaz Moerman
  • Published 15 August 2020
  • Mathematics
  • Journal of Number Theory
In recent years, Rogers and Zudilin developed a method to write $L$-values attached to elliptic curves as periods. In order to apply this method to a broader collection of $L$-values, we study Eisenstein series and determine their Fourier series at cusps. Subsequently, we write the $L$-values of an elliptic curve of conductor 32 as an integral of Eisenstein series and evaluate the value at $k>1$ explicitly as a period. As a side result, we give simple integral expressions for the generating… Expand

References

SHOWING 1-10 OF 37 REFERENCES
Regulator of modular units and Mahler measures
  • W. Zudilin
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
  • 2014
Abstract We present a proof of the formula, due to Mellit and Brunault, which evaluates an integral of the regulator of two modular units to the value of the L-series of a modular form of weight 2 atExpand
Intégrales régularisées et fonctions L de formes modulaires via la méthode de Rogers–Zudilin [Regularized integrals and L-functions of modular forms via the Rogers–Zudilin method
  • These de doctorat
  • 2020
Many Variations of Mahler Measures
The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, specialExpand
Many variations of Mahler measures: a lasting symphony
  • Aust. Math. Soc. Lecture Ser. 28
  • 2020
Periods
Zudilin, Many variations of Mahler measures: a lasting symphony
  • Aust. Math. Soc. Lecture Ser
  • 2020
Regulators of Siegel units and applications
We present a formula for the regulator of two arbitrary Siegel units in terms of L-values of pairwise products of Eisenstein series of weight one. We give applications to Boyd's conjectures andExpand
On the Mahler Measure of 1+X+1/X+Y +1/Y
.The study of multi-variable Mahler measures originated in the work of Smyth, whoproved relations with Dirichlet L-values and special values of the Riemann zetafunction [22]. Formula (1) is the firstExpand
Identities for the Ramanujan zeta function
TLDR
Formulas for special values of the Ramanujan tau zeta function are proved and it is shown that L(@D,k) is a period in the sense of Kontsevich and Zagier when k>=12. Expand
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