Rosh Hashanah 4:10 part 4

Mishnah

Just like the Shaliach Tzibbur is obligated, so too is everyone else.

Rabban Gamliel says: The Shaliach Tzibbur fulfills the obligation on behalf of the masses.

Yerushalmi

Rebbi Chunah and Rabbah of Tzipporin in the name of Rebbi Yochanan: The halachah is like Rabban Gamliel for those blows (אלין תקיעתא).  Rebbi Zeirah and Rav Chisda were sitting there for the shofar blows, and when they finished their prayers, Rav Chisdah got up again to pray.  Rebbi Zeirah said to him: Did we not already say the prayers?  He replied: I prayed and I need to pray again.  When they came down from Arbayim and they say there in the name of Rebbi Yochanan: The halachah is like Rabban Gamliel for those shofar blows, and I did not have kavanah (and therefore I need to pray again).  And if I would have had proper kavanah, I would have already fulfilled my obligation.

(Background: It seems from this that a person could say Musaf for Rosh Hashanah without the Malchuyot, Zichronot, and Shofarot, and then fulfill the obligation of those blessings only by listening to the Shaliach Tzibbur, and this was the intent of Rav Chisdah, whereas Rebbi Zeirah was going to rely entirely on the Shliach Tzibbur, per the Ran on the Rif here.)

Rebbi Zeira said: and it is good that all the tannaim taught it in the name of Rabban Gamliel, and Rebbi Hoshayah taught it in the name of Chachamim.

Rebbi Adda of Keisarin said in the name of Rebbi Yehudah: And this (ruling regarding relying on the Shaliach Tzibbur is dependent on) a person being there from the beginning of the prayer (i.e. he must listen carefully for the entire prayer).  Rebbi Tanchum son of Rebbi Yirmiyah said: The Mishnah taught as such: The order of the prayer is first Avot, Gevurot, and then Kedushat Hashem (i.e. it must be the entire prayer from the beginning).

Hadran Alach Masechet Rosh Hashanah

Bavli (34b-35a)

The conclusion here is that the halachah is like Rabban Gamliel for the blessings of Malchuyot, Zichronot, and Shofarot of Rosh Hashanah and Yovel's Yom Kippur, but the rest of the year, it is a disagreement.

Rabban Gamliel would also say that the Shaliach Tzibbur would fulfill the obligation for even those that couldn't come to the synagogue to hear the blessings.  Specifically those that lived outside of the city, but those that could have come, are not included.  We learn this also by Bircat Cohanim, where a person needs to be standing in front of the cohen, but the blessing includes those that are in the fields because they are busy with their work and cannot come to the synagogue.

Hadran Alach Masechet Rosh Hashanah