A second similar explanation is based on the Gemara (Shabbos 89:), which teaches that the Sinai Desert has five names. One is פארן מדבר, which comes from the words ורבו פרו, to bear children. Rashi writes, נתעברה אחד דכל רמיזא היכא ידענא ולא ,לאהליכם לכם שובו במצות זכר אשתו. This means that all women became pregnant with boys after matan Torah. If we count nine months from the day after matan Torah (סיון 'ז), we arrive at אדר 'ז. All children were born on אדר 'ז, and there was a big shalom zachor that week in the desert.
Toras Avos writes in the name of the Yesod HaAvodah that Shabbos Zachor is mesugal for the barren to be blessed with children because about Rachel it states (Bereishis 30:22), רחמה את ויפתח ...רחל את אלקים ויזכור, "Hashem remembered Rachel...and opened her womb." And by Sarah it states (Bereishis 21:1), 'וה ותלד ותהר ...שרה את פקד ," Hashem remembered Sarah... and she became pregnant, and she bore a child." The Beis Avraham teaches that זכור and פקד, which both mean "remember," are used in reference to Hashem remembering Sarah and Rachel to grant them children, and when discussing Amalek, the two terms זכור and פקד are used again. It states את זכור עמלק לך עשה אשר , and it states in the haftarah, עמלק לך עשה את פקדתי, "I remember what Amalek did to you." This tells us that Shabbos Zachor is mesugal to be remembered for children.
Similarly, Rebbe Tzadok HaCohen (Divrei Sofrim #29) writes, “I learned from my teachers that Shabbos Zachor is mesugal for bearing children..." He explains that on Shabbos Zachor, we read about destroying Amalek so that he wouldn't have offspring. The rule is that Klal Yisrael blossoms from Amalek's downfall, as it states (Yechezkel 26:2), החרבה אמלאה, "I shall become full from the destroyed city." Rebbe Tzadok HaCohen writes, "Yaakov and Eisav are opposites. When one is destroyed, the other flourishes. We understand that when Amalek's offspring are cut off, the Yidden's offspring will increase."
Tefillah on Taanis Esther
The Kav HaYashar (ch.97) quotes the Beis Yosef’s magid, “Hashem’s hashgachah is always over Bnei Yisrael. They are His lot, His chosen nation, and He desires to grant them Olam Haba. Therefore, when the 14th of Adar approaches, the day the Jewish nation is extremely happy with the miracles that Hakadosh Baruch Hu performed for them, that he brought the downfall of the rasha Haman and his children and the other resha’im of that time... and Chazal say, ‘one is obligated to be happy with wine on Purim,’ therefore, Hakadosh Baruch Hu commanded us to fast before Purim because fasting is a segulah to be saved from sin. Fasting causes that the Satan shouldn’t be mekatreg and lead the Jewish nation to sin due to abundant eating and drinking.
"It is therefore important to have kavanah in the selichos on taanis Esther when we say the piyut מספר במתי. The final stanza of this selichos is תיפלה והעבר תפילה שומע, ‘Listen to our prayers and remove sin...’ When saying these words, have kavanah that you shouldn’t sin, chas veshalom, due to the eating and drinking and festivities of Purim.”
The Kav HaYashar further teaches that taanis Esther is an auspicious day for tefillah for all our needs. He writes, “People from the villages should come to the city, so they can daven in a beis knesses on taanis Esther because taanis Esther is very mesugal for our tefillos to be answered in the merit of Mordechai and Esther. Whoever needs a salvation should take the time to say Tehillim chapter 22, “השחר אילת,” and afterward pour out his heart in prayer before Hashem to request his needs and to rouse the merit of Mordechai and Esther. In their merit, Hashem will listen to his tefillos, open the gates of compassion, and answer his tefillos. Therefore, beloved people of Hashem, the holy nation, who gather to listen to megillah on Purim... Arouse Mordechai and Esther’s merits because taanis Esther and Purim are days of ואהבה רצון, desire and love. It is good to pray on taanis Esther, and the One who listens to prayers will compassionately answer your tefillos, amen.”