We have for is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue to which the Hecke series is attached. This result yields the new bound
On a pour est le premier coefficient de Fourier de forme de Maass correspondant à la valeur propre à laquelle le série de Hecke est attachée. Ce résultat fournit l’estimation nouvelle
@article{JTNB_2001__13_2_453_0, author = {Aleksandar Ivi\'c}, title = {On sums of {Hecke} series in short intervals}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {453--468}, publisher = {Universit\'e Bordeaux I}, volume = {13}, number = {2}, year = {2001}, doi = {10.5802/jtnb.333}, zbl = {0994.11020}, mrnumber = {1879668}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.333/} }
TY - JOUR TI - On sums of Hecke series in short intervals JO - Journal de Théorie des Nombres de Bordeaux PY - 2001 DA - 2001/// SP - 453 EP - 468 VL - 13 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.333/ UR - https://zbmath.org/?q=an%3A0994.11020 UR - https://www.ams.org/mathscinet-getitem?mr=1879668 UR - https://doi.org/10.5802/jtnb.333 DO - 10.5802/jtnb.333 LA - en ID - JTNB_2001__13_2_453_0 ER -
Aleksandar Ivić. On sums of Hecke series in short intervals. Journal de Théorie des Nombres de Bordeaux, Volume 13 (2001) no. 2, pp. 453-468. doi : 10.5802/jtnb.333. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.333/
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